Let X be a continuous random variable with pdf f(x) =...

Let X be a continuous random variable with pdf f(x) = { k/x^4, x > 1 0, x <= 1 A. Determine the value of k for which f(x) is a legitimate pdf B. Obtain the cumulative distribution function. C. Use the cdf from (b) to determine the probability that X is greater than 2 D. Obtain the expected value and variance of X.

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:07 Let me put this small for you.

00:10 Now in this question we can consider a continuous random variable and we are given the density of the function fx here.

00:21 In the part i will need to determine the value of the case for which fx is a pdf.

00:27 We might to you that in that you be a bdf, the integral of the fx d x from infinity to infinity must equal to one therefore to do the part a here we want to find the integral of here for the x greater than one we get equal to this one so it will be from one to infinity then we have the k over x power for the x now to serve this one and we bring the k outside and we have the one to infinity.

01:05 One over x power 4 we can write as x power minus 4 d x.

01:10 Therefore untie derivative of that equals to x power minus 3 over minus 3, evaluate from 1 to infinity.

01:19 So we get infinity inside got the 0.

01:22 If we put the 1 inside, we get the k over minus 3, k over 3.

01:28 And then this one we need to put this one equal to 1 therefore we should see that k must equal to 3 so we found the k equal to 3 therefore the fx equal to 3 over x power 4 for the x greater than 1 now for the part p once you obtain the cumulative distribution function so denoted by the capital f x is equal to the probability between the x smaller equal to the small x.

02:03 So i check the integral from 1 to x, and this one will be the 3 over, we replace the x by the t power 4 d t.

02:13 Therefore this one just equal to the 3, and then we will have entire derivative of that equal to the t power minus 3 over minus 3.

02:27 And then evaluate this one from 1 to 1 to 2.

02:30 X so we get equal to the it will put the one in second one and if we put the x in so we got the minus x power minus 3 or we can write this down to the 1 minus 1 of x power 3 and this one for the x squared than 1 so this will be the cumulative distribution function now for the c want you use the cdf from be to determine the probability that the x greater than 2.

03:05 So this one will be the same as the complement 1 minus the complement x minor equal to 2...

Question

Please give Ace some feedback