Say we have a continuous random variable X with density function f(x)=c(1+x3) (where c is a...

Say we have a continuous random variable X with density function f(x)=c(1+x3) (where c is a constant)with support SX =[0,3].

a.) What value of c will make f(x) a valid probability density function.

b. )What is the probability that X=2? What is the probability that X is greater than 2?

Now say we have an infinite sequence of independent random variables Xi (that is to say X1, X2, X3, ....) with density f(x) stated earlier.

c. What is the probability that the first random variable/trial to be greater than 2 is on the 10 trial (first 9 trials are less than 2 and the 10 trial is greater than 2) ?

d. What is the probability that it will take less than 10 random variables/trials before we see a trial that is greater than 2?

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Expert Solution

The solutions to the given problems are in the pictures attached

orchestra answered 1 year ago

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