3 |
5 |
7 |
9 |
11 |
13 |
48 |
c = 1/48
e)
x | p | min(9,x) | |
3 | 0.0625 | 3 | 0.1875 |
5 | 0.104167 | 5 | 0.520833 |
7 | 0.145833 | 7 | 1.020833 |
9 | 0.1875 | 9 | 1.6875 |
11 | 0.229167 | 9 | 2.0625 |
13 | 0.270833 | 9 | 2.4375 |
48 | 1 | 7.916667 |
E(min(9,X)) = 7.9167
f)
x | p | (X - 9)+ | |
3 | 0.0625 | 0 | 0 |
5 | 0.104167 | 0 | 0 |
7 | 0.145833 | 0 | 0 |
9 | 0.1875 | 0 | 0 |
11 | 0.229167 | 2 | 0.458333 |
13 | 0.270833 | 4 | 1.083333 |
48 | 1 | 1.541667 |
E((X-9)+) = 1.54167
4. Let X be a discrete random variable with Pr(X i} = ci for positive, odd...
Let X be a discrete random variable with Pr{X = i} = ci for positive, odd integers 3 ≤ i ≤ 13; otherwise, the probability is zero. (a) Compute E[min(9,X)]. (b) Compute E[(X − 9)+] where x+ = max(x, 0).
4. Let X be a discrete random variable with PrX-ici for positive, odd integers 3 Sis 13; otherwise, the probability is zero a) Compute the value of c. (b) What is the mean of X? (c) What is the second moment of X (that is, E[X21)? (d) What is the variance of X? (e) Compute E[min(9, X) (f) Compute E(X-9)*) where x+ = max(x,0).
4. Let X be a discrete random variable with PrXici for positive, odd integers 3 3i s 13 otherwise, the probability is zero (a) Compute the value of c. (b) What is the mean of X? (c) What is the second moment of X (that is, E[X2])? (d) What is the variance of X? (e) Compute E[min(9, X)]. (f) Compute E[(X - 9)+] wherea+max(x, 0)
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discrete random variable has probability mass function, P(X = n) = ?1?n. ? 1, forxeven Let Y = −1, for x odd Find the expected value of Y ; (E[y]). probability function mass A discrete random variable has P ( X = n) = (3) for x Y = { for Find the expected value of Y CE(y)] Let even x odd