Given that X is a random variable having a Poisson(A) distribution, compute the following: (a) Р(X — 1) when A %3 5.5 Р(X — 1) — (b) P(X < 7) when A = 3.5 Р(X < 7) 3 (c) P(X > 7) when A = 4 P(X > 7) = | (d) P(X < 5) when A = 5.5 %3| Р(X < 5) -

A child gets a weekly allowance (a certain non-negative number of dollars). The amount (in dollars) is random with expectation equal to 6 and variance equal to 6. Let’s denote this random variable by X. I want to estimate (from above) the chances that the child gets 10 dollars or more on a given week. In other words, I want to find c such that P(X ≥ 10) ≤ c, with c that is as small as possible.(a) Use the Markov inequality to find c such that P(X ≥ 10) ≤ c.(b) Use the Chebyshev inequality for the variance to find c such that P(X ≥ 10) ≤ c.(c) Read about the one-sided Chebyshev inequality, and use it to find c such that P(X ≥ 10) ≤ c.