Let Z ∼ N (0, 1), and let X = max(Z, 0). 1. Find FX in...

Question

Question

Let Z ∼ N (0, 1), and let X = max(Z, 0).

1. Find FX in terms of Φ(t). Is X a continuous random variable ?

2. Compute p(X = 0)

3. Compute E(X). Hint: use the CDF expectation formula, and integration by parts. You may assume that limt t nφ(−t) = 0 for all n ≥ 0.

4. Find the CDF FX2 (u)

5. Compute V(X). Hint: use FX2 , and follow the same hint of part (3)

math Statistics-And-Probability

Answer 1

Answer #1

Answer 2

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