I\'m finishing up my stochastics homework and I am not sure what this question i

Question

I'm finishing up my stochastics homework and I am not sure what this question is asking/how to solve it. If anyone could give me some help and explain what it's asking I would be so very appreciative. THANKS

Question # 6

A         If a Poisson distributed RV, x is such that its probability at (x = 0) is equal to the probability at: (x = 1) plus   3 × probability at (x = 2). Find the mean of x.

In a statistically large number of enumerated wireless connectivity, x depicts the statistics of call failures with an expected mean, mo = 50. Assume that x shows a strong central tendency towards its mean value; and, the corresponding standard deviation, so = 14.

            Suppose, the calls are randomly monitored and the sampled observation shows 49 call failures. Mostly xL = 30 such failures are on the lower side and xU = 70 failures on the upper side of the sampled mean value. Construct the normalized distribution of Z, p (Z) versus Z showing ZsL; and ZsU

Explanation / Answer

Solution

Back-up Theory

If X ~ Poisson with parameter (mean), then its pmf is given by

p(x) = e – (x)/(x!) …………………………………………………………..(1)

Now, to work out the solution,

The given information, put in probability terminology, is:

P(X = 0) = P(X = 1) + 3.P(X = 2). …………………………………………..(2)

(1)/(1!) + 3.(2)/2 = 1or 32 + 2 – 2 = 0

=> = {- 2 ± (4 + 24)}/6 = 0.549 [note cannot be negative]

So, mean of X = 0.549 ANSWER

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