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Outcomes of a random variable

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1. Suppose that all of the outcomes of a random variable are  , and that P(a)=P(b)=P(c)=P(d)= 1/4, (that is, all outcomes a, b, c, and d each have a 1/4 probability of occuring), and P(e)=0. Define the events  ,  ,  , and  . True or false: The events A and C are independent.

True

False

2. Suppose that all of the outcomes of a random variable are  , and that P(a)=P(b)=P(c)=P(d)= 1/4, (that is, all outcomes a, b, c, and d each have a 1/4 probability of occuring), and P(e)=0. Define the events  a={a,b}, b={b,c}, c={c,d}, and d={e}. Calculate the probability p(a/c).

a- 1/2

b- 1/8

c-0

d-1/3

3. If the coefficient of correlation r=0.80 the standard deviations of x and y are 2 and 0.5, respectively. Then Cov(x,y) must be

a-1.6

b-0.8

c-0.08

d-8

4. Suppose that all of the outcomes of a random variable are  , and that P(a)=P(b)=P(c)=P(d)= 1/4, (that is, all outcomes a, b, c, and d each have a 1/4 probability of occuring), and P(e)=0. Define the events  ,  ,  , and  . True or false: The events A and B are independent.

5. Consider a binomial random variable where the probability of success on each trial is 0.7, and there are 10 different trials. what is the probability of having more than 5 successes?/

a-0952

b-0.048

c-0.849

d-0.151

Reference no: EM131868853

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