Question

Find the expected value of the random variable g(X) = X² . where the discrete random vartable X has the probiabily distribution given bolow

f(x) = ( 3/x )( 3/7)ˣ (4/7)³−ˣ ,x=0,1,2,3 The expected value of g(X) = X² is 1260/343.

Answer 1

The expected value of the random variable g(X) = X², with the provided probability distribution, can be found by multiplying each value of X² by its probability and summing the products.

Step-by-step explanation:

The expected value of the random variable g(X) = X², where the discrete random variable X has the probability distribution f(x) = ( 3/x )( 3/7)ˣ (4/7)³−ˣ ,x=0,1,2,3, can be found by multiplying each value of X² by its probability and adding the products:

E(g(X)) = Σ (X²)(3/X)(3/7)ˣ(4/7)³−ˣ

By substituting the values of X and using the given probability distribution, we can calculate the expected value as 1260/343.