Question

Assume that suppX = {−2, −1, 0, 1, 3} and P(X = −2) = P(X = −1)

= P(X = 0) = P(X = 1) = P(X = 3). Let Y = X4 . Find the
distribution of Y .

Answer 1

The distribution of Y, where Y = X^4, is {16, 1, 0, 81} with equal probabilities.

Step-by-step explanation:

To find the distribution of Y, we need to determine the possible values of Y and their corresponding probabilities. Since Y = X^4, we need to calculate the value of X^4 for each value in the support of X. Given that suppX = {-2, -1, 0, 1, 3} and P(X = -2) = P(X = -1) = P(X = 0) = P(X = 1) = P(X = 3), we can calculate the distribution of Y as follows:

• When X = -2, Y = (-2)^4 = 16
• When X = -1, Y = (-1)^4 = 1
• When X = 0, Y = 0^4 = 0
• When X = 1, Y = 1^4 = 1
• When X = 3, Y = 3^4 = 81

Since each value of X has the same probability, P(Y = 16) = P(Y = 1) = P(Y = 0) = P(Y = 81). Therefore, the distribution of Y is: {16, 1, 0, 81} with probabilities P(Y = 16) = P(Y = 1) = P(Y = 0) = P(Y = 81).