Let B ∼ Ber(0.3) and U ∼ Unif[0, 1] be independent random variables. a) For any...

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Let B ∼ Ber(0.3) and U ∼ Unif[0, 1] be independent random variables. a) For any...

Let B ∼ Ber(0.3) and U ∼ Unif[0, 1] be independent random variables.

a) For any x ∈ R find the cdf FX(x) of X = B · U
using the law of total probability
FX(x) = P(X ≤ x) = P(X ≤ x|B = 0)P(B = 0) + P(X ≤ x|B = 1)P(B = 1)
and exploiting the independence of U and B.

b) Is X a continuous random variable?

c) Find FX(.5) and P(0 < X < .8).

d) Find q such that P(X ≤ q) = .8.

math Statistics-And-Probability

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