# 50+ Solved Probability Distribution MCQs – Statistics

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### Probability Distribution MCQs

Mean of continuous uniform (Rectangular) distribution is.
A.(ß+a)/2
B.(ß-a)/2
C.(ß-a)/4
D.?(ß-a)?^2/12

A.(ß+a)/2

Mean deviation of continuous uniform (Rectangular) distribution is.
A. (ß+a)/2
B. (ß-a)/2
C. (ß-a)/4
D. ?(ß-a)?^2/12

C. (ß-a)/4

If 0 A. 1
B. 1/?
C. ?
D. None of these

B. 1/?

?(1-?t)?^(-1)ism. g. f of.
A. Uniform distribution
B. Gamma distribution
C. Beta distribution
D. Negative Exponential distribution

D. Negative Exponential distribution

Mean deviation of Negative Exponential distribution is.
A. ?(1-?t)?^(-1)
B. 1-e^(?-x/?_? )
C. 2?e^(-1)
D. ?^2

C. 2?e^(-1)

Mean of Negative Exponential distribution is.
A. ?(1-?t)?^(-1)
B. 1-e^(?-x/?_? )
C. 2?e^(-1)
D. ?

D. ?

Mode of Negative Exponential distribution is.
A. ?(1-?t)?^(-1)
B. Does not exist
C. 2?e^(-1)
D. ?

B. Does not exist

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Range of the distribution is 0 to 8 of.
A. Gamma distribution
B. Beta distribution of kind II
C. Negative Exponential distribution
D. All of these

D. All of these

If a = 1 then Gamma distribution becomes.
A. Uniform distribution
B. Beta distribution of kind II
C. Negative Exponential distribution
D. Laplace distribution

C. Negative Exponential distribution

If ß = 1, mean and variances become same of.
A. Uniform distribution
B. Beta distribution of kind II
C. Negative Exponential distribution
D. Gamma distribution

D. Gamma distribution

?aß?^2is variance of.
A. Uniform distribution
B. Beta distribution of kind II
C. Gamma distribution
D. Negative Exponential distribution

C. Gamma distribution

Mean of Gamma distribution is.
A. (a-1)ß
B. aß
C. (a-1)ß2
D. aß2

B. aß

(a-1)ß is mode of.
A. Uniform distribution
B. Beta distribution of kind II
C. Gamma distribution
D. Negative Exponential distribution

C. Gamma distribution

A distribution having five parameters is called.
A. Gamma distribution
B. Bivariate normal distribution
C. Beta distribution of kind II
D. Negative Exponential distribution

B. Bivariate normal distribution

a and ß are two parameters of.
A. Gamma distribution
B. Laplace distribution
C. Bivariate normal distribution
D. Negative Exponential distribution

a and ß are two parameters of.

?(1-ßt)?^(-a)is m.g.f of.
A. Uniform distribution
B. Beta distribution of kind II
C. Gamma distribution
D. Negative Exponential distribution

C. Gamma distribution

Mode is (l-1)/(l+m-2) of.
A. Gamma distribution
B. Beta distribution of kind I
C. Beta distribution of kind II
D. None of these

B. Beta distribution of kind I

0=x=1is range of.
A. Gamma distribution
B. Laplace distribution
C. Beta distribution of kind II
D. Beta distribution of kind I

D. Beta distribution of kind I

f(x) = 1/(ß(l,m)) ?x^(l-1) (1-x)?^(m-1), 0=x=1 is pdf of.
A. Gamma distribution
B. Laplace distribution
C. Beta distribution of kind I
D. All of these

C. Beta distribution of kind I

Mean is l/(m-1) of.
A. Laplace distribution
B. Beta distribution of kind II
C. Beta distribution of kind I
D. Gamma distribution

B. Beta distribution of kind II

Mode is (l-1)/(m+1) of.
A. Beta distribution of kind I
B. Laplace distribution
C. Beta distribution of kind II
D. Gamma distribution

C. Beta distribution of kind II

Variance is (l(l+m-1))/((m-1)^2 (m-2)) of.
A. Beta distribution of kind II
B. Laplace distribution
C. Beta distribution of kind I
D. Gamma distribution

A. Beta distribution of kind II

If f(x) = 1/2 e^(-|x| ), -8=x=8 then its variance is.
A. 4
B. 2
C. 0
D. None of these

B. 2

If f(x) = 1/2 e^(-|x| ), -8=x=8 then its mean deviation is.
A. 4
B. 2
C. 1
D. 0

C. 1

Range of Cauchy distribution is.
A. -8 to 8
B. 0 to ?
C. 0 to 8
D. -1 to +1

A. -8 to 8

Mode is v(1/2?) of.
A. Beta distribution of kind I
B. Laplace distribution
C. Beta distribution of kind II
D. Rayleigh distribution

D. Rayleigh distribution

Mean of ?2 distribution is.
A. 2n
B. n-2
C. n
D. 8n

C. n

Mode of ?2 distribution is.
A. 2n
B. n-2
C. n
D. 8n

B. n-2

If a = n/2 and ß = 2 then Gamma distribution becomes.
A. ?2 distribution
B. F- distribution
C. t- distribution
D. Beta distribution

A. ?2 distribution

If zi’s are independent standard normal variates then ?_(i=1)^n¦z_i^2 ~.
A. t- distribution
B. F- distribution
C. ?2- distribution
D. Beta distribution

C. ?2- distribution

?^2?normality if.
A. n?8
B. n?0
C. n?10
D. n?1

A. n?8

Which distribution becomes standard Cauchy distribution if n = 1.
B. F- distribution
C. ?2- distribution
D. t- distribution

D. t- distribution

Mean is zero of.
A. Beta distribution
B. F- distribution
C. t- distribution
D. ?2- distribution

C. t- distribution

Variance is n/(n-2) of.
A. Beta distribution
B. t- distribution
C. F- distribution
D. ?2- distribution

B. t- distribution

All odd order moments about origin/Mean are zero of.
A. Beta distribution
B. F- distribution
C. t- distribution
D. ?2- distribution

C. t- distribution

If n ?8 then t ?.
A. Normal
B. Gamma
C. Beta
D. Laplace

A. Normal

If x ~ F(n_1,n_2) then ……..~ F(n_2,n_1 ).
A. x2
B. 1/x
C. ?2
D. None of these

B. 1/x

n1andn2 are degrees of freedom of.
A. Beta distribution
B. t- distribution
C. F- distribution
D. ?2- distribution

C. F- distribution

F- distribution has.
A. Two parameters
B. Three parameters
C. Four parameters
D. None of these

A. Two parameters

0 to 8 is range of.
A. F- distribution
B. ?2- distribution
D. All of these

D. All of these

Variance of F-distribution exists for.
A. n2> 2
B. n2> 4
C. n2> 1
D. None of these

B. n2> 4

Mean of F-distribution exists for.
A. n2> 2
B. n2> 4
C. n2> 1
D. None of these

A. n2> 2

ß(l,m) =?_0^1¦?x^(l-1) (1-x)?^(m-1) dx is called.
A. Gamma function
B. Beta function of II kind
C. Beta function of I kind
D. None of these

C. Beta function of I kind

Which distribution is positively skewed.
A. Normal distribution
B. ?2- distribution
C. t- distribution
D. None of these

B. ?2- distribution

If y1 = y2 = y3 then first order statistics is.
A. y3
B. y2
C. y1
D. None of these

C. y1

If f(x) = e-x, 0 A. e-x
B. 1- e-x
C. e-x -1
D. None of these

D. None of these

If y1 = y2 = y3 then median is.
A. y3
B. y2
C. y1
D. None of these

A. y3

Which is order statistics.
A. A. M
B. Median
C. G. M
D. H. M

B. Median

To check the strength of a chain, we study.
A. Largest order statistics
B. Middle order statistics
C. Smallest order statistics
D. Mode