Question

9) Let $X \sim \text{Bernoulli}(0.4)$ and $Y \sim \text{Bernoulli}(0.3)$ be independent. Define $Z = X + Y - XY$, find the distribution of $Z$. Bernoulli(0.28) Bernoulli(0.72) Bernoulli(0.58) Bernoulli(0.42)

          9) Let $X \sim \text{Bernoulli}(0.4)$ and $Y \sim \text{Bernoulli}(0.3)$ be independent. Define $Z = X + Y - XY$, find the distribution of $Z$.
Bernoulli(0.28)
Bernoulli(0.72)
Bernoulli(0.58)
Bernoulli(0.42)

9) Let X ∼Bernoulli(0.4) and Y ∼Bernoulli(0.3) be independent. Define Z = X + Y - XY, find the distribution of Z.
Bernoulli(0.28)
Bernoulli(0.72)
Bernoulli(0.58)
Bernoulli(0.42)

Added by Donna W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Supreeta N

05/11/2023

Step 1

To find the distribution of Z, we need to find the probability mass function (PMF) of Z. Z can take on the values -1, 0, and 1. When Z = -1, it means both X and Y are 1. The probability of this happening is P(X=1) * P(Y=1) = 0.4 * 0.3 = 0.12. When Z = 0, it Show more…

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9) Let X ~ Bernoulli(0.4) and Y ~ Bernoulli(0.3) be independent. Define Z = X + Y - XY. Find the distribution of Z. 4) Let X ~ Bernoulli(0.4) and Y ~ Bernoulli(0.28), Z ~ Bernoulli(0.72), W ~ Bernoulli(0.58), and V ~ Bernoulli(0.42) be independent. Define Z = X + Y - XY. Find the distribution of Z.