probability a ticket is an instant winner is 30%. You purchase 10 tickets. What

Question

probability a ticket is an instant winner is 30%. You purchase 10 tickets. What is the probability: a. Exactly 2 will be winners? b. Less than 3 will be winners? c. At least 1 will be a winner? d. What is the average number of winners? Find: 2. Suppose A and B are events with PIA) 0.4, P(B)06, PAUB)-0.8. Fi a. Draw a Venn Diagram for this situation. Make sure you label an b. the probability that A does not occur C. P(AnB) d. P(AlB) e. P(BIA) f. P(BIA) (probability of B given not A) g. Are the events A and B independent? Explain how you know. 3. Given the distribution of a discrete random variable in the table. 0.2 0.1 fs) 0.3 0.4 a. Find the mean of X, E(X). b. Find the variance of X, Var(x). variables X and Y 4. Given below the joint distribution hlyofthe discrete rand a. Find the marginal distribution functions for X andy b. Are the random variables X and Y independent? c. Find the covariance of X and Y, Cov(x,Y Explain how you know 0 1/9 1/9 1/9 2/9

Explanation / Answer

Solution:-

p = 30/100

p = 0.30

a) The probability that exactly 2 will be winners is 0.2335.

x = 2, n = 10

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 2) = 0.2335

b) The probability that less than 3 will be winners is 0.3828.

x = 3, n = 10

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 3) = 0.3828.

c) The probability that atleast 1 will be a winner is 0.9718.

x = 1, n = 10

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 1) = 0.9718.

d) The average number of winners is 3.0.

E(x) = n*p

E(x) = 10 × 0.30

E(x) = 3.0

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