The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2x + 4 0

The proportion of people who respond to a certain mail-order solicitation is a<br>continuous random variable X that has the density function<br>(2x + 4<br>0 < x<1<br>f(x) =<br>0,<br>5<br>elswhere<br>a. Verify that f(x) is a density function.<br>b. Show that P(0<X<1) =1.<br>c. Find F(x) the cumulative distribution function<br>d. Find the probability that more than 1/4 but fewer than 1/2 of the people<br>contacted will respond to this type of solicitation.<br>e. Find the expectation E[X] and Var(X) of the random variable X.<br>

Extracted text: The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2x + 4 0 <><1 f(x)="0," 5="" elswhere="" a.="" verify="" that="" f(x)="" is="" a="" density="" function.="" b.="" show="" that=""><><1) =1.="" c.="" find="" f(x)="" the="" cumulative="" distribution="" function="" d.="" find="" the="" probability="" that="" more="" than="" 1/4="" but="" fewer="" than="" 1/2="" of="" the="" people="" contacted="" will="" respond="" to="" this="" type="" of="" solicitation.="" e.="" find="" the="" expectation="" e[x]="" and="" var(x)="" of="" the="" random="" variable="">

Jun 03, 2022

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The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2x + 4 0

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