MA2631-Conference 4 Solved

1.    Consider the random variable X with the probability mass distribution

                             P[X = −1] = 0.3,              P[X = 2] = 0.5,              P[X = 5] = 0.1,              P[X = 10] = 0.1.

Calculate the expected value and variance of X as well as the expectation of Y with Y = eX.

2.    Let X be a Poisson distributed random variable with parameter λ = 2.

a)    Calculate

P[X ≥ 2|X ≥ 1].

b)    Calculate

 .

3.    Let Y be a Poisson distributed random variable with parameter λ, where λ is a non-negative integer. Calculate

E [ |Y − λ| ].

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