It is advisable to have working smoke detectors in your apartment. In fact, JJ Smoke Detectors...

It is advisable to have working smoke detectors in your apartment. In fact, JJ Smoke Detectors Advisors (JJSDA) analyzes the numbers of smoke detectors in apartments. Suppose X is the number of smoke detectors in a randomly selected apartment. Then according to JJSDA, x has the following probability mass function, p(x), and cumulative distribution function F(x).

x	0	1	2	3	4	5
p(x)	.119	.171	.35	.20	b	.03
F(x)	.119	a	.640	.840	.970	1.00

a. If F is the cumulative distribution function of x, then what is the value of a?
b. If p is the probability mass function for x, then evaluate b. c) What is the expected value of x <_>
c. What is the expected value of x?
d. Calculate the standard deviation of x.
e. What is the variance of .5x?
f. JJSDA checks 9 apartments on a Tuesday. What is the probability that there are exactly 3 smoke detectors in exactly 3 of the checked apartments?
g. JJSDA checks 5 apartments on a Wednesday. What is the probability that all 5 of those apartments have at least 2 smoke detectors?
h.What is the expected value of

x³

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Expert Solution

orchestra answered 1 year ago

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