3. The number of injections using a needle contaminated with the AIDS virus that is required to detect an exposure to the virus is denoted here as the random variable X, and it follows the following probability distribution: 1 2 3 4 5 P(X=x) .45 .35 .10 .05 .05 a. Find the expected number of injections required for the detectable exposure of the virus, E(X). b. Find the variance of the random variable X. c. Let X and Y denote the number of injections using AIDS contaminated needles for each of two people, respectively, where X and Y both follow the distribution above. Further, assume that X and Y are statistically independent. What is the probability that both exhibit a detectable exposure after only one injection?
3. The number of injections using a needle contaminated with the AIDS virus that is required to detect an exposure to the virus is denoted here as the random variable X, and it follows the following probability distribution: 1 2 3 4 5 P(X=x) .45 .35 .10 .05 .05 a. Find the expected number of injections required for the detectable exposure of the virus, E(X). b. Find the variance of the random variable X. c. Let X and Y denote the number of injections using AIDS contaminated needles for each of two people, respectively, where X and Y both follow the distribution above. Further, assume that X and Y are statistically independent. What is the probability that both exhibit a detectable exposure after only one injection?
MATLAB: An Introduction with Applications
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Transcribed Image Text:3. The number of injections using a needle contaminated with the
AIDS virus that is required to detect an exposure to the virus is denoted here as the
random variable X, and it follows the following probability distribution:
1
2
3
4
5
P(X=x)
.45
.35
.10
.05
.05
a. Find the expected number of injections required for the detectable exposure of the
virus, E(X).
b. Find the variance of the random variable X.
c. Let X and Y denote the number of injections using AIDS contaminated needles
for each of two people, respectively, where X and Y both follow the distribution
above. Further, assume that X and Y are statistically independent. What is the
probability that both exhibit a detectable exposure after only one injection?
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