Suppose that X1;X2;X3 are independent normal random variables with means 10; 11;

Question

Suppose that X1;X2;X3 are independent normal random variables with means 10; 11; 15 (re-

spectively), and standard deviations 2; 5; 1 (respectively). Let Y = 3X1 + X2 - 2X3. Calculate

Please do show the steps since i already have the asnwer not sure where im messing up and not getting right answer! Thx

thx

Problem 2 The truss is simply supported with a pin at A and a roller support at H. The truss supports two loads, each of magnitude L, at pins E and F. Determine the forces in members DG, CD, DF and DE. Be sure to state if the members are in tension (T) or compression (C. 2R 22.5

Explanation / Answer

here mean for Y=3*10+11-2*15=11

and std deviation =((3*2)2+(5)2+(-2*1)2)1/2=8.0623

hence P(10<Y<11.5)=P((10-11)/8.0623<Z<(11.5-11)/8.0623)=P(-0.12<Z<0.06)=0.5239-0.4522=0.0717

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