Question

Consider a random variable with the following pmf: f(x)=c 1/2x , for x=0,1,2,3. a. Find c so that f(x) represents a valid probability distribution. b. Find μ = E(X). c. Find σ2 = V ar(X). d. Find E(X2).

Answer 1

The question is about determining a constant for a valid pmf and computing mean, variance, and expected square for a discrete random variable with specified probabilities.

Step-by-step explanation:

The student's question concerns finding parameters for a valid probability mass function (pmf) and calculating statistical quantities such as expected value, variance, and expected square. The variable X defines a discrete random variable that takes on values 0 through 3 with respective probabilities determined by the function f(x) = c (1/2)^x. To ensure f(x) is a valid pmf, the sum of probabilities over all possible values of X must equal 1. This condition is used to solve for c. The expected value μ = E(X) is the mean of the distribution, defined as the sum of each value of X multiplied by its corresponding probability. The variance σ^2 = Var(X) measures the spread of the random variable around the mean, calculated using the expected value of X and the expected value of X^2. To find the expected square E(X^2), we sum the square of each value of X multiplied by its corresponding probability.