110年 - 110 國立中山大學碩士暨碩士專班招生考試_通訊所碩士班/甲組:機率#105733

2. Let A₁, A₂, A₃ be events in a sample space . Let P(A₁) = 0.4, P(A₂) = 0.2, P(A₃) = 0.4, and AinA . Let B be another event with = 0.05. What is? (A) 0.8 (B) 0.4 (C) 0.1 (D) 0.08 (E) None of these

3.Consider two random variables X and Y with joint pdf
Which of the following statements is correct? (A) E[X]=1/2 (B) P(X+Y≤1)=1/2 (C) E[XY]=1/3 (D) Xand Y are uncorrelated (E) X and Y are independent f(x,y)=段古

4. Let U be uniformly distributed over [0,1]. Which of the following statements is wrong? (A) E[U]=1/2 (B) Var(U)= 1/12 (C)Let Y = -In (U). The pdf of Y is. (D) Let Z = e^U. The pdfofZ is f(z) = 1/z, for 1 ≤ z ≤ e. (E) The MGF of U is

5. Consider two independent random variables X₁ and X₂ with Poisson distribution: Which of the following statements is wrong? (A) The mean of X_i is λ_i (B) The variance of Xi is 1/ λ_i (C) The moment generating function of X_i is(D) X₁ + X₂ is Poisson distributed (E) None of these

7. If the pdf of a continuous random variable is given as
, what is the value of P(X = 1)? (A) 0 (B) 1/4 (C) 1/3 (D) 1/2 (E) 1

9. Let X be a random variable with a moment generating function of the form 'What is the variance of X ? (A)0 (B) 1 (C) (D) (E)