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6. The diameter of electric cables, say X, is assumed to be a continuous random variable with probability density function (pdf): f(x) = { ke^(-1/3x) for x > 0, 0 otherwise } a. find expected value of random variable X b. Find V(X) c. standard deviation of X c. Find cumulative distribution function for X

          6. The diameter of electric cables, say X, is assumed to be a continuous random variable with probability density function (pdf):
f(x) = { ke^(-1/3x) for x > 0, 0 otherwise }
a. find expected value of random variable X
b. Find V(X)
c. standard deviation of X
c. Find cumulative distribution function for X

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6. The diameter of electric cables, say X, is assumed to be a continuous random variable with probability density function (pdf):
f(x) = ke^(-1/3x) for x > 0, 0 otherwise
a. find expected value of random variable X
b. Find V(X)
c. standard deviation of X
c. Find cumulative distribution function for X

Added by Dean M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

09/12/2023

Step 1

Since the integral is over the positive values of X only, we can write: E(X) = ∫0∞ x (1/2) dx = [x^2/4]0∞ = ∞/4 = ∞ Show more…

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The diameter of electric cables, say X, is assumed to be a continuous random variable with probability density function (pdf): f(x) = 1/x for x > 0, otherwise 0. a. Find the expected value of the random variable X. b. Find V(X). c. Find the standard deviation of X. d. Find the cumulative distribution function for X.

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