1. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate E(X)
X  P(X) 
0  0.1 
1  0.1 
2  0.1 
3  0.4 
4  0.1 
5  0.2 
2. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate the variance of X
X  P(X) 
0  0.1 
1  0.1 
2  0.1 
3  0.4 
4  0.1 
5 
0.2 
3. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate the standard Deviation of X
X  P(X) 
0  0.1 
1  0.1 
2  0.1 
3  0.4 
4  0.1 
5 
0.2 
4. Given 2 independent and not mutually exclusive events, A and B, with probabilities given on the right, calculate the probability that A and B occurs.
P(A) =  0.3 
P(B) =  0.8 
P(A/B)=  0.3 
P(B/A)= 
0.8 
5. Given 2 events, A and B, with probabilities given on the right, calculate the probability that A and B occurs. Events A and B are not independent and also not mutually exclusive
P(A)=  0.800 
P(B)=  0.600 
P(A/B)=  0.833 
P(B/A)= 
0.625 
6. Given 2 events, A and B, that are independent and not mutually exclusive with probabilities given on the right, calculate the probability that A or B occurs.
P(A)=  0.8 
P(B)= 
0.3 
7. Given 2 events, A and B, that are not independent but mutually exclusive with probabilities given on the right, calculate the probability that A or B occurs.
P(A)=  0.5 
P(B)=  0.1 
8. Given a binomial random variable, X = # successes, where the sample size (n) and the probability of a success (p) are given on right, calculate P(X < a) where "a" is given on the right.
n =  20 
p =  0.3 
a =  2 
9. Given a binomial random variable, X = # successes, where the sample size (n) and the probability of a success (p) are given on right, calculate P(X > a) where "a" is given on the right.
n =  20 
p =  0.2 
a =  7 
10. Given a binomial random variable, X = # successes, where the sample size (n) and probability of a success (p) are given on right, calculate P(a < X < b) where "a" and "b" are given on the right.

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