The MGF identifies masses1/6,1/3,1/3,1/6 at0,1,2,3 respectively. Adding the first three gives1/6+1/3+1/3=5/6, D. The remaining1/6 is the probability at3.
More Random Variables and Transforms questions
GATE 2020 ST Q26– X has characteristic function φ(t)=sin(t)cos(t)/t for t≠0 and φ(0)=1. Find P( X ≤3/2) (two…
GATE 2026 ST Q14– Independent discrete X,Y have M X(t)=(1+2e(−t)+3e(2t))/6 and M (X+Y)(t)=(2+eᵗ+3e(3t))/6.…
GATE 2026 ST Q30– Continuous X has CDF F. Let Y=−3ln F(X). Find E(Y) (integer).
GATE 2025 ST Q28– X has CDF F with lim (h→0−)F(3+h)=1/4 and F(3)=3/4. Find 16P(X=3) (integer).
GATE 2025 ST Q39– X has CDF 0 for x<0, α(1+2x²) for 0≤x<1 and 1 for x≥1. Its median is 1/√2. Find α.
GATE 2025 ST Q58– Independent X,Y,Z have MGFs M X(t)=(2+eᵗ)²/9,M Y(t)=exp(eᵗ−1),M Z(t)=exp[2(eᵗ−1)]. Find…