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

Say we have a continuous random variable X with density f(x) = c (1+x³) (where c is a constant) with support S_x = [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 X_i (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

orchestra answered 1 year ago

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