b) Find the variance of profit per automobile V(X). 1/18 2/9 2/27 3/18
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B.1) Let the random variable X represent the number of automobiles that are used for official business purposes on any given workday. The probability distribution for company A is x: 1, 2, 3 pA(x): 0.3, 0.4, 0.3 and for company B is x: 0, 1, 2, 3, 4 pB(x): 0.2, 0.1, 0.3, 0.3, 0.1 Compute the variances for both companies, and compare them. B.2) The percentage of impurities per batch in a certain type of industrial chemical is a random variable X having the probability density function f(x) = {12x^2 (1 - x); 0 ≤ x ≤ 1 0; otherwise a) Suppose a batch with more than 40% impurities cannot be sold. What is the probability that a randomly selected batch will not be sold? b) Suppose the dollar value of each batch is given by V=5-0.5X. Find the expected value and variance of V.
Sri K.
Let the random variable X represent the number of automobiles that are used for official business purposes on any given workday. The probability distribution for company A is x | 1 2 3 f(x) | 0.3 0.4 0.3 and that of for company B is x | 0 1 2 3 4 f(x) | 0.2 0.1 0.3 0.3 0.1 Show that the variance of the probability distribution for company B is greater than that for company A.
Ivan K.
A dealer's profit, in units of $\$ 5000,$ on a new automobile is a random variable $X$ having density function $$ f(x)=\left\{\begin{array}{ll} 6 x(1-x), & 0 \leq x \leq 1 \\ 0, & \text { elsewhere } \end{array}\right. $$ (a) Find the variance of the dealer's profit. (b) Demonstrate that Chebyshev's theorem holds for $k=2$ with the density function above. (c) What is the probability that the profit exceeds $\$ 500 ?$
Mathematical Expectation
Chebyshev's Theorem
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