Question 1 Let X denote the number of computers sold during a particular week by a certain store. The probability mass function (pmf) of X is given as follows: \begin{tabular}{c|ccccc} $x$ & 0 & 1 & 2 & 3 & 4 \\ $p(x)$ & 0.10 & 0.20 & 0.30 & 0.25 & 0.15 \\ \end{tabular} Moreover, 60% of all customers who purchase these computers also buy an extended warranty. Let Y denote the number of purchasers during this week who buy an extended warranty. Tasks 1. Find $P(X = 4; Y = 2)$. 2. Calculate $P(X = Y)$. 3. Determine the joint pmf of X and Y. 4. Find the marginal pmf of Y.
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Let X denote the number of brand X VCRs sold during a particular week by a certain store. The pmf of X is Seventy percent of all customers who purchase brand X VCRs also buy an extended warranty. Let Y denote the number of purchasers during this week who buy an extended warranty. a. What is P(X = 4, Y = 2)? [Hint: This probability equals P(X = 4) · P(Y = 2|X = 4). Now think of the four purchases as four trials of a binomial experiment, with success on a trial corresponding to buying an extended warranty.] b. Calculate P(X = Y).
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