Answer: Option c

Explanation:

Here, first, we need to find mean

= 31+97+112+12= 315/5 = 63

Standard deviation = [1/n (x(n)-mean)²]^0.5

= 25.79

Answer: Option b

Explanation: Mode = The value that appears most frequent; here, the number 13 repeated twice.

Answer: Option d

Explanation:

Where,

n = number of terms = 7

The median is the middle value of the data sets, so first, we need to arrange the number in ascending order 11,13,13,17,19,23,25

the middle one is 7+1/2 = 4^th number

so, the 4^th number is 17

Answer: Option c

Explanation: Mode = The value that appears most frequent = 7 which is repeated twice. And,

Where n = number of terms = 9

The median is the middle value of the data sets, so first, we need to arrange the number in ascending order 7,7,8,11,12,14,21,23,27

the middle one is 9+1/2 = 5^th number

so, the 5^th number is 12

Answer: Option b

Explanation: In sampling distribution, the Mean of a number is equal to the Mean of the sampling distribution; hence the Mean of the number is 18 the Mean of the sampling distribution is 18.

Answer: Option b

Explanation:

Given,

P = 0.8

q = 1-p

= 1 – 0.8

=0.2

Therefore, mean = q = 0.2

And we know that variance = pq = (0.2) (0.8) = 0.16

Answer: Option q

Explanation:

Given,

p= 80% = 0.8 and q = 1-p = 20% = 0.2 and n= 12

Therefore,

Mean= np = (12)(0.8) = 9.6

And,

Variance = npq = (9.6)(0.2)= 1.92

Answer: Option b

Explanation:

Here, p = ½ and q = ½

N = 4

Therefore, Mean = np = 4*1/2 = 2

Answer: Option a

Explanation:

We know that, V(a) = E (x²) – (E(a)²)

= x²– x² = 0

Answer: Option b

Explanation: In Poisson’s distribution, a positive constant called λ is used, which is the mean and variance of the distribution. The Poisson distribution predicts how many of a certain type of event will occur in a bounded area or during a given period, provided that the events occur independently and cannot occur simultaneously. The events are sometimes called “outcomes” or “observed occurrences.”

Answer: Option c

Explanation: The mean of the constant x is x.

Answer: Option d

Explanation: We know that, E(x) = x P(x) = 0.8*3 = 2.4

Answer: Option a

Explanation: We know the formula of Poisson’s distribution,

Answer: Option d

Explanation: We know the formula of Poisson’s distribution,

Answer: Option b

Explanation:

We know that,

E(X) = 0(1/7) + 1(2/7) + 2 (3/7) + 3(4/7) + 4(5/7)

0 + 2/7 + 6/7 + 12/7 + 20/7

= 5.71

Answer: Option b

Explanation: For a discrete probability distribution, the variance is given by the following equation

Answer: Option a

Explanation: A Poisson distribution with mean k is given by Variance = k

Therefore,

Standard Deviation = √variance = √k

Answer: Option c

Explanation: If we want to calculate the AM, we need to find the total number in the data set. In the given question, total number = 5

Answer: Option c

Explanation:

In the given question, the total number is 4, so by using the formula to determine the geometric Mean, we have,

G.M = (1×3×9×3)^1/4

= (81)^1/4

= (3⁴)^1/4

= 3

Answer: Option d

Explanation: If we want to calculate the variance, the first thing you need to do is find the Mean of the given data set,

Therefore,

Then, we need to find the Variance V = (3-6)² + (9-6)² + (5-6)² + (6-6)² + (7-6)²/5

= 9+9+1+0+1 /5 = 20/5 = 4

Answer: Option d

Explanation:

Mean = (5+8+12+13+12+14+6+8+12+10)/ 10 = 10

Mode = Mode is the most repeated value of the given data set.

= 12 (12 repeated 3 times in the set of data)

For median, first we need to arrange the value in ascending order in the given data set: 5,6,8,8,10,12,12,12,14,17. Here, the numbers 10 and 12 are the middle values. The average of the given number is 12+10/2 = 11. Hence, 11 is the median for the given data set. So, the value of Mean, mode, and median are 10,12,11

Answer: Option b

Explanation:

Mean = (9+13+5+9+6+5+9)/7 = 56/7 = 8

Mode = Mode is the most repeated value of the given data set. = 9 (repeated 3 times in the set of data)

For median, first, we need to arrange the value in ascending order in the given data set: 5,5,6,9,9,9,13. Here, the number 9 is placed in the middle. Hence, 9 is the median for the given data set. So, the value of Mean, mode, and median are 8,9,9

Answer: Option b

Explanation:

Range = Maximum Value – Minimum Value

Here, Maximum value in the data sets = 96, and Minimum value = 2

Therefore, Range = 96-2 = 94

Answer: Option b

Explanation:

If we want to calculate the mean deviation according to the Mean. First, we need to calculate the Mean of the given data sets

Therefore, Mean = 7+47+8+42+47+95+42+96+3/9 = 43

Now, we need to find the deviation to calculate mean deviation i.e.,

(43-7) +(47-43) +(43-8) +(43-42) +(47-43) +( 95-47) +(43-42) +(96-43) +(43-3) = 222

So,

Answer: Option c

Explanation:

If we want to calculate the mean deviation according to the median, first, we need to calculate the median of the given data sets

Therefore, to calculate the median, first, we need to arrange the number in ascending order 3,7,8,42,42,47,47,95,96

SO, Median = 42

Now, we need to find the deviation to calculate mean deviation according to median i.e.,

(42-3) +(47-7) +(42-8) +(42-42) +(42-42) +( 47-42) +(47-42) +(95-42) +(96-42) =

So,

Answer: Option c

Explanation:

If we want to calculate the variance, first, we need to calculate the Mean of the given data sets

Therefore, Mean = 7+47+8+42+47+95+42+96+3/9 = 43

Now, we need to find the square of deviation to calculate variance i.e.,

(43-7)² +(47-43)² +(43-8)² +(43-42)²+(47-43)² +( 95-47)² +(43-42)² +(96-43)²+(43-3)² =

=1296+16+1225+1+16+2304+1+2809+1600

=9268

So,

Answer: Option c

Explanation:

If we want to calculate the standard deviation, first, we need to calculate the Mean of the given data sets

Therefore, Mean = 7+47+8+42+47+95+42+96+3/9 = 43

Now, we need to find the square root to calculate the variance i.e.,

(43-7)² +(47-43)² +(43-8)² +(43-42)²+(47-43)² +( 95-47)² +(43-42)² +(96-43)²+(43-3)² =

=1296+16+1225+1+16+2304+1+2809+1600

=9268

Answer: Option b

Explanation:

If we want to calculate the coefficient, we need to calculate the Mean of the given data sets.

Therefore,

Mean = 7+47+8+42+47+95+42+96+3/9 = 43

Now, we need to find the square root to calculate the variance i.e.,

(43-7)² +(47-43)² +(43-8)² +(43-42)²+(47-43)² +( 95-47)² +(43-42)² +(96-43)²+(43-3)² =

=1296+16+1225+1+16+2304+1+2809+1600

=9268

So,

Answer: Option a

Explanation:

Given,

Probability (P) = ¼

And we know that,

λ = np = (8) × ¼ = 2

Answer: Option a

Explanation: The Mean of any data sets refers to the sum of the function in its domain multiplied with random variables’ value. Therefore, the Mean is given by E(K), where k is a random variable.

Answer: Option a

Explanation:

Let f(x) be the random variable of the given function X

Now, E(k) = ∫kf(x)

= kf(x)

= k(1) = k

Answer: Option b

Explanation:

Variance (V) = E(k²) – (E(K))²

= k²– k² = 0

Answer: Option a

Explanation: If we consider a discrete function, the variance is given by the following equation

If we consider a discrete function, the variance is given by the following equation

Variance(V) = ∑_(x=0)^Zx² X(x) – µ²

Here,

µ = Mean

When we substitute X(x) = z_Cx X^x y^(z-x) in the above equation and µ = zx we get

Variance = xyz.

Answer: Option c

Explanation:

Poisson distribution is usually applied for discrete random variables along with Binomial distribution. The Poisson distribution expresses the probability of a given number of events occurring in a fixed interval of time and space if these events occur with a known average rate and independently since the last event.

As a result, the distribution is often used in counting processes where the average rate of the events happening is known, and individual events occur independently of each other.

Answer: Option a

Explanation: We know the formula of Poisson’s distribution,

Answer: Option a

Explanation:

Mean = Total sum of the number of given data sets/ Total number in data sets

(3+8+12+17+16+14+6+8+16+10)/ 10 = 11

Answer: Option c

Explanation:

Mode = Mode is the most repeated value of the given data set.

= 12 (12 repeated 5 times in the set of data)

Answer: Option c

Explanation: For median, first, we need to arrange the value in ascending order in the given data set: 2,5, 6,7, 8,8,12,13,14,17. Here, the numbers 8 and 8 are the middle values. The average of the given number is 8+8/2 = 8. Hence, 8 is the median for the given data set.

Answer: Option b

Explanation:

Given,

Probability P = 0.4

q = 1-p

= 1 – 0.4

=0.6

Therefore, Mean = q = 0.6

And we know that Variance = pq = (0.4) (0.6) = 0.24

Answer: Option d

Explanation: If we want to calculate the AM, we need to find the total number in the data set. In the given question, total number = 7

Answer: Option c

Explanation:

If we want to calculate the variance, first we need to find the Mean of the given data set,

Therefore,

Then, we need to find the Variance (V) = (5-4)² + (7-5)² + (6-5)² + (5-3)² + (7-5)² + (5-3)²/6

= 1 + 4 + 1 + 4 + 4 +4/6 = 18/3 = 6

Answer: Option c

Explanation:

According to the property of Expectation

Variance V(X) = K(X²) – (K(X))²

Answer: Option b

Explanation:

Integrating f(x) = X² from 0 and 4 we get the value of K(X²) = 64

Answer: Option d

Explanation:

Where n = number of terms = 5

The median is the middle value of the data sets, so first, we need to arrange the number in ascending order 21,35,44,45,55

the middle one is 5+1/2 = 3rd number

so, the 3rd number is 44

Answer: Option b

Explanation:

If we want to calculate the standard deviation, first, we need to calculate the Mean of the given data sets

Therefore, Mean = 7+2+8+11+6+13+16/7 = 63/7 = 9

Now, we need to find the square root to calculate the variance = (Mean – each number of data sets)²

i.e.,

(9-7)² +(9-2)² +(9-8)² +(9-11)²+(9-6)² +( 13-9)² +(16–9)²

=4 + 49 + 1 + 4 + 9 + 16 + 49

=132

So,

Answer: Option d

Explanation:

If we want to calculate the standard deviation, first, we need to calculate the Mean of the given data sets

Therefore, Mean = 7+2+8+11+6+13+16/7 = 63/7 = 9

Now, we need to find the square root to calculate the variance = (Mean – each number of data sets)²

i.e.,

(9-7)² +(9-2)² +(9-8)² +(9-11)²+(9-6)² +( 13-9)² +(16–9)²

=4 + 49 + 1 + 4 + 9 + 16 + 49

=132

So,

Answer: Option d

Explanation:

Given

Variance (A) = 0.4 and Variance (B) = 0.6

And K = 4A – 2B

Therefore,

Var(K) = Var(4A – 2B)

= Var(4A) + Var(2B)

= 16 Var(A) + 4 Var(B)

Var(K) = 16*0.4 + 4*0.6

= 8.8

Answer: Option c

Explanation:

The equation gives the Mean of the Hypergeometric distribution

E(X) = n*k/N

Where,

N denotes the number of trails

K denotes the number of success

And, N denotes the sample size

Answer: Option a

Explanation:

The variance of the Hypergeometric distribution is given by n* k (N-k)*(N-n)/[N²*(N-1)].

Where,

n denotes the number of trails

K denotes the number of success

An, N denotes the sample size.

Answer: Option b

Explanation:

We know that,

Range = Maximum Value – Minimum Value

Here, Maximum value in the data sets = 99, and Minimum value = 17

Therefore, Range = 99-17= 82