A discrete random variable X is defined by the following probability distribution
| X | 2 | 7 | 9 | 10 |
|---|---|---|---|---|
| P ( X = x ) | 0.08 | 0.12 | 0.38 | 0.42 |
Find the following :
μ = E ( X )
E(X^2) .
E ( 2X + 3 )
E ( 4X − 8 )
σ ^2 = Var ( X )
σ = SD ( X )
TOPIC:Discrete random variable and Expected values,variance and sd.


A discrete random variable X is defined by the following probability distribution X 2 7 9...
The table below shows the probability distribution of a discrete random variable X. Values of the random variable X (x) Probability of observing each value of X P(X = x) 6 0.20 7 0.25 8 0.25 9 0.10 10 0.12 11 0.08 Total 1.00 (a) Determine the probability that the random variable X is between 8 and 10, inclusive. (1 mark (b) Determine the probability that the random variable X is at least 9. (1 mark) c. Determine the probability...
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1. The probability distribution of a discrete random variable X is given by: P(X =-1) = 5, P(X = 0) = and P(X = 1) = ? (a) Compute E[X]. (b) Determine the probability distribution Y = X2 and use it to compute E[Y]. (c) Determine E[x2] using the change-of-variable formula. (You should match your an- swer in part (b). (d) Determine Var(X).
The number of homes sold by a realtor during a month has the following probability distribution: Number Sold Probability 0 0.10 1 0.40 2 0.50 The standard deviation of the number of homes sold by the realtor during a month is the closest to _______. A) 0.44 B) 1.40 C) 0.66 D) 1.35 The standard deviation of the discrete random variable X is calculated as SD(X)=σ=σ2−−√.SD(X)=σ=σ2. The variance of the discrete random variable X is calculated as Var(X) = σ2=∑(xi–μ)2P(X=xi).
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