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Return to the scenario described in the previous problem. Suppose an individual purchases25 boxes of this cereal. (a) Let $X_{1}=1$ if at least one type 1 toy is included in the 25 boxes and $X_{1}=0$ otherwise(a Bernoulli rv). Determine $E\left(X_{1}\right) .$(b) Define $X_{2}, \ldots, X_{10}$ analogously to $X_{1}$ for the other nine types of toys. Express the number of different toys obtained from the 25 boxes in terms of the $X_{i}$ s and determine its expected value.(c) What happens to the expected value in $($ b) as the number of boxes purchased increases? Asthe number of different toys available increases?(d) Show that, for $i \neq j$$\operatorname{Cov}\left(X_{i}, X_{j}\right)=\left(\frac{8}{10}\right)^{25}-\left(\frac{9}{10}\right)^{50}$Then determine the variance of the number of different toys obtained from the 25 boxes byapplying Eq. $(4.5)$ to the expression from part (b). [Hint: Refer back to Example 4.19 forthe required method.]

Intro Stats / AP Statistics

Chapter 4

Joint Probability Distributions and Their Applications

Section 11

Supplementary Exercises

Probability Topics

The Normal Distribution

University of North Carolina at Chapel Hill

Oregon State University

University of St. Thomas

Lectures

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Okay in this question in this question, we have to let x be containing them variable, which has moment m t equal to e, raise to the power 4 into e, raise to the power y minus t by poison table. We have probability mu minus 2, seen x, mu plus 2. Sin goes as property 0 x on to inweave, raised to the power minus 4 by this minus 44 s to the bottom and pie 1 factorial up to minus 44 raised to the power even by 7. Factorial minus is to our 4 per 0 divided by 0. We give the answer .931 as a required answer. Is probability? U minus 2 c o a x? U plus 2 equals to 0.931. Thank you.

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