A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of number of success is _____________

(a)

\(\frac { 8 }{ 3 } \)

(b)

\(\frac { 3 }{ 8 } \)

(c)

\(\frac { 4 }{ 5 } \)

(d)

\(\frac { 5 }{ 4 } \)

Var (2x ± 5) is =________

(a)

5

(b)

var (2x) ± 5

(c)

4 var (X)

(d)

0

If the p.d.f. \(f(x)=\{ \begin{matrix} \cfrac { x }{ 2 } ,0 then \(\\ \\ \\ E\left( { 3x }^{ 2 }-2x \right) \) =_______.

(a)

\(\frac { 2 }{ 3 } \)

(b)

\(\frac { 4 }{ 3 } \)

(c)

\(\frac { 10 }{ 3 } \)

(d)

\(\frac { 7 }{ 3 } \)

The variance of a binomial distribution is________.

(a)

equal to its mean

(b)

less than its mean

(c)

greater than its mean

(d)

none

In a binomial distribution n = 4, \(P(X=0)=\frac { 16 }{ 81 } \) then P(X = 4) is __________.

(a)

\(\frac { 1 }{ 16 } \)

(b)

\(\frac { 1 }{ 81 } \)

(c)

\(\frac { 1 }{ 27 } \)

(d)

\(\frac { 1 }{ 8 } \)

A coin is tossed 3 times. The probability of getting exactly 2 heads is________

(a)

\(\frac { 1 }{ 2 } \)

(b)

\(\frac { 1 }{ 8 } \)

(c)

\(\frac { 3 }{ 8 } \)

(d)

\(\frac { 1 }{ 4 } \)

The sum of the mean and variance of a binomial distribution for 6 total is 2.16. Then the probability of success p =__________

(a)

0.4

(b)

0.6

(c)

0.8

(d)

0.2

If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to__________.

(a)

\(\frac { 5 }{ 16 } \)

(b)

\(\frac { 11 }{ 16 } \)

(c)

\(\frac { 10 }{ 16 } \)

(d)

\(\frac { 1 }{ 2 } \)

A die is thrown 10 times. Getting a number greater than 3 is considered a success. The S.D of the number of successes is _________

(a)

2.5

(b)

1.56

(c)

5

(d)

25

If x is a continuous random variable then \(P\left( x\ge a \right) =\) __________.

(a)

\(P(x < a)\)

(b)

\(1-P(x>a)\)

(c)

\(P(x>a)\)

(d)

\(1-P(x\le a-1)\)

If x is a continuous random variable then P(x ≥ a) = ________

(a)

\(P(x \ < \ a)\)

(b)

\(P(a\le x\le b)\)

(c)

\(P\left( x>a \right) \)

(d)

\(1-P\left( x\le a-1 \right) \)

If X is a continuous random variable then which of the following is incorrect?

(a)

F'(x) = f(x)

(b)

\(F(\infty )=1,F(-\infty )=0\)

(c)

\(P(a\le X\le b)=F(b)-F(a)\)

(d)

\(P(a\le X

If F(x) is a distribution function of a random variable then the false statement is ____________

(a)

\(F(\infty )=1\)

(b)

\(F(-\infty )=-1\)

(c)

\({ F }^{ ' }\left( x \right) =f(x)\)

(d)

\(0<\mathrm{F}(x)<1\)

If the mean and S.D of a binomial distribution are 12 and 2 respectively, then ___________

(a)

npq = 4

(b)

\(q=\frac { 1 }{ 3 } \)

(c)

\(P=\frac { 2 }{ 3 } \)

(d)

\(pq=\frac { 1 }{ 9 } \)

A random variable X has the following probapality mass function?

X	-2	3	1
P(X = x)	\(\frac { \lambda }{ 6 } \)	\(\frac { \lambda }{ 4 } \)	\(\frac { \lambda }{ 12 } \)

Then __________ 

(a)

\(\frac { \lambda }{ 6 } +\frac { \lambda }{ 4 } +\frac { \lambda }{ 12 } =1\)

(b)

\(\lambda =2\)

(c)

\(P(X=3)=\frac { 1 }{ 8 } \)

(d)

\(P(1\le X\le 3)=\frac { 2 }{ 3 } \)