3.19 Show that 1 -za-le-²dz = a = 1, 2, 3, .... y! y=0 (Hint: Use integration by parts.) Express this formula as a probabilistic relationship between Poisson and gamma random variables.
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- The fire department of a city wants to test the null hypothesis that σ =10 minutes for the time it takes a fire truck to reach a fire site against thealternative hypothesis σ 6= 10 minutes. What can it conclude at the 0.05 levelof significance if a random sample of size n = 48 yields s = 9.5minutes?Suppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?To test Upper H 0: mu equals 60 versus Upper H 1: mu less than60, a random sample of size N equals 25 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
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