Given independent random variables with means and standard deviations as shown,

Question

Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables SD a) 3X d) 2X-5Y a) Hind the mean and standard deviation tor the random variable 3x b) 3Y 5 e)xX2 Mean 80 15 SD(3X)- (Round to two decimal places as needed.) b) Find the mean and standard deviation for the random variable 3Y+5 SD(3Y+5) (Round to two decimal places as needed.) c) Find the mean and standard deviation for the random variable 5X+4Y (Round to two decimal places as needed.) d) Find the mean and standard deviation for the random variable 2X-5)Y E(2X-5Y)- SD(2X-5Y)-

Explanation / Answer

GIVEN

.Mean.......St.Dev.
X.....80..............11
Y.....15...............4

a) E(3X) = 3E(X)= 3*80=240

SD(3X)=3SD(X)=3*11=33

b) E(3Y+5)=3E(Y)+5= 3*15+5=50

SD(3Y+5)=3SD(Y)+5=3*4+5=17

c)E(5X+4Y)=5E(X)+4E(Y)=5*80+4*15=460

SD(5X+4Y)= SQRT(5^2 * 11^2+4^2*4^2)=SQRT(3025+256)= SQRT3281 =57.28

d)E(2X-5Y)=2E(X)-E(Y)=2*80-15= 145

SD(2X-5Y)=SQRT(2^2*11^2+5^2*4^2)=SQRT(484+400)=SQRT884=29.73

e)E(X1+X2)= E(X1)+E(X2) = 2E(X)=2*80=240

SD(X1+X2)=SQRT(11^2+11^2)=SQRT242=15.55

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