MHT CET202521 Apr 2025Evening ShiftMathematicsProbabilityActual
A random variable X has p.m. f. P ( X =x)= ^4 C _x 2^4 , x=0,1,2,3,4 and and ^2 are mean and variance respectively of random variable X , then
Options
- A=2, ^2=4
- B=2, ^2=1
- C=3, ^2=4
- D=2, ^2=5
Correct answer
B. =2, ^2=1
Step-by-step solution
The probability mass function P(X=x) = 4 x 2^4 corresponds to a binomial distribution where the number of trials is n=4 and the probability of success is p = 1 2 . The mean of a binomial distribution B(n, p) is = np = 4 1 2 = 2 . The variance is ^2 = np(1-p) = 4 1 2 1 2 = 1 . Comparing with the options, the solution is B .