3. The density function of the continuous random variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is given in Exercise 3.7 on page 92 as f(x) = { x, 0 < x < 1, 2 - x, 1 ? x < 2, 0, elsewhere. } Find the average number of hours per year that families run their vacuum cleaners. 4. Find the proportion X of individuals who can be expected to respond to a certain mail-order solicitation if X has the density function f(x) = { 2(x+2)/5, 0 < x < 1, 0, elsewhere. }
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First, we need to find the expected value (average) of the random variable X. The expected value of a continuous random variable is given by the integral of x*f(x) over the range of x. Show more…
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The probability distribution of the discrete random variable X is f(x) = (3/x)(1/4)^x(3/4)^(3-x), x = 0, 1, 2, 3. find the mean of X. 3. The density function of the continuous random variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is given in Exercise 3.7 on page 92 as f(x) = {x, 0 < x < 1; 2-x, 1 <= x < 2; 0, elsewhere. Find the average number of hours per year that families run their vacuum cleaners. 4. Find the proportion X of individuals who can be expected to respond to a certain mail-order solicitation if X has the density function f(x) = {2(x+2)/5, 0 < x < 1; 0, elsewhere.
Sri K.
The density function of the continuous random variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is f(x) = { x/16, 0 < x < 4 5 - x, 4 ≤ x < 5, 0, elsewhere. For both parts (a) and (b) below, express your final answers in hours. (a) Find the average number of hours per year that families run their vacuum cleaners. (b) Find the standard deviation of the number of hours per year that families run their vacuum cleaners.
David N.
The total time, measured in units of 100 hours, that a teenager runs their hair dryer over a period of one year is a continuous random variable $X$ that has the density function $$ f(x)=\left\{\begin{array}{ll} x, & 0<x<1 \\ 2-x, & 1 \leq x<2 \\ 0, & \text { elsewhere } \end{array}\right. $$ Use Theorem 4.6 to evaluate the mean of the random variable $Y=60 X^{2}+48 X,$ where $Y$ is equal to the number of kilowatt hours expended annually.
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