1 answer

All my work is wrong, except for what's in red. can you please work it out...

Question:

3. Suppose the length of time. X. required by students to complete a hour exarm is a random variable with p.d.f. 0 elsewhere (a) Find the constant c (b) Find EX) d(e) Find V(x). -D.12 ( 06 20 .0 % 2 2 - 0.21x0 12

All my work is wrong, except for what's in red. can you please work it out step by step

3. Suppose the length of time. X. required by students to complete a hour exarm is a random variable with p.d.f. 0 elsewhere (a) Find the constant c (b) Find EX) d(e) Find V(x). -D.12 ( 06 20 .0 % 2 2 - 0.21x0 12

Answers

a) f(x)=cx^2+x, We know Integrate(f(x)dx)=1, thus (cx^2+x)dx=1 [You pulled the constant c out but it is attached only with x^2] or cx^3/x+x^2/2|(0,1)=1, which gives

c/3+1/2=1 or c/3=1/2 and c=3/2.

b)E(x)=x*f(x)dx from (0,1) or (3/2*x^3+x^2)dx=3/8*x^4+x^3/3|(0,1)=3/8+1/3=17/24=0.708

c) Var(x)=E(x^2)-(E(x))^2. E(x^2)=x^2f(x)dx=(3/2*x^4+x^3)dx=3/10*x^5+x^4/4|(0,1)=3/10+1/4=11/20

Thus Var(x)=11/20-(17/24)^2=0.048

.

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