Question

#5 please

2. Find the probability distribution function for the random variable representing picking a random real number between -1 and 1. (This is a piecewise defined function.) 3. Compute the mean of the random variable with density function if x>0 ed f(r) = if r < 0. 0 4. Compute the mean of the random variable with density function 2e (1 - cos x) if x >0 if r<O. f (x) = 5 Compute the variance and standard deviation of the random variable with density function 1 -x if x|1 if a > 1. f(x) = 0 6. Compute the variance and standard deviation of the random variable with density function if Jx - 11<1 O if Ja-1> 1. { f (x)

Answer 1

Given funchion 1-121, 21 1- fox) f(r)=L-120) When -12EI furthar aimpiby If When -1 X 40 when 142 17 X Phen when fx)1-2 .The function 12 1XEO Can be n Hen as 1-21

daviation and To find stondard variance fird first need mean we M Elx) ob 11 j -1 o dx+ L2)(x) dr -79 (x) dx -1 ob weceewao ( 22 11 -1 () e- 2

Variance fu-232de o dr t 1 1 f + 1 Variance Standard deviation Vasiance 1