Suppose that Y1 is a binomial random variable with four

Chapter 6, Problem 97SE

(choose chapter or problem)

Suppose that $Y_{1}$ is a binomial random variable with four trials and success probability .2 and

that $Y_{2}$ is an independent binomial random variable with three trials and success probability

.5. Let $W=Y_{1}+Y_{2}$. According to Exercise 6.53(e), W does not have a binomial distribution.

Find the probability mass function for W. W.

[Hint:

$P(W=0)=P\left(Y_{1}=0, Y_{2}=0\right) ; P(W=1)=P\left(Y_{1}=1, Y_{2}=0\right)+P\left(Y_{1}=0, Y_{2}=1\right)$; etc.]

Equation Transcription:

${Y}_{1}$

${Y}_{2}$

$W={Y}_{1}+{Y}_{2}$

$P(W=0)=P({Y}_{1}=0,\ {Y}_{2}=0);\ P(W=1)-P({Y}_{1}=1,\ {Y}_{2}=0)+P({Y}_{1}=0,\ {Y}_{2}=1)$

Text Transcription:

W=Y1+Y2

P(W=0)=P(Y1=0, Y2=0); P(W=1)-P(Y1=1, Y2=0)+P(Y1=0, Y2=1)

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