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A) Suppose that a radio tube inserted into a certain type of set has probability of 0.2 of functioning more than 500 hours. If we test 20 tubes, what is the probability that exactly 5 of these functions more than 500 hours.
B) A continuous random variable X has the following probability density function:
For A), use the Poisson distribution. M. Poisson was a French mathematician whose name also happens to mean "fish" in French. To those who disagreed with him, M. Poisson said, "One man's meat is another man's Poisson!"
If you tested 20 tubes many times, on average 4 of them would last more than 500 hours (.20 of 20). The formula you need for the probability of exactly 5 lasting more than 500 hours is
This is not so hard to compute. 4^5 is 1024, and 5! is 120. So we have
For B), I don't whether (1 - x) is in the exponent or is a factor of multiplication. Please clarify with parentheses or asterisks.
I see that math girl is using the latter, wherein (1 - x) is a factor of the multiplication. In that case, I agree with her that A = 12, for the reason she gives that the integral from 0 to 1 is equal to 1. She gives you the expression for the integral so you should be able to find the value of it over the interval 1/3 to 1/2. If not, choose this answer as best and ask me to integrate your expression from 1/3 to 1/2 for you.
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