(a) A continuous random variable X is distributed according to a probability den- sity function (pdf) fx(x) = c (1+ x), -1
(a) A continuous random variable X is distributed according to a probability den- sity function (pdf) fx(x) = c (1+ x), -1
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![(a) A continuous random variable X is distributed according to a probability den-
sity function (pdf)
fx(x) = c (1+ x), -1<r<1 (and fx (x) = 0 elsewhere)
where c is a constant to be determined.
(i) State the conditions for fx(r) to be a pdf and show that c =
= 1/2.
(ii) Find the first, E(X), and the second ordinary moment, E(X?), and hence
find the mean and variance of X.
(iii) Find the Moment Generating Function G(t) for X and express it in the
simplest form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe14b533c-9841-4969-9d1a-a9bb8c6b327f%2F3fd7a016-3424-4192-a996-27040f9e0476%2Frz62tc7k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) A continuous random variable X is distributed according to a probability den-
sity function (pdf)
fx(x) = c (1+ x), -1<r<1 (and fx (x) = 0 elsewhere)
where c is a constant to be determined.
(i) State the conditions for fx(r) to be a pdf and show that c =
= 1/2.
(ii) Find the first, E(X), and the second ordinary moment, E(X?), and hence
find the mean and variance of X.
(iii) Find the Moment Generating Function G(t) for X and express it in the
simplest form.
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