Question

3. Let X be a continous random varialile. a. What valoe of e will make () valil deay? [부 ]: .. b, what is P(X 1)? mu 3% c cona..suo dus.ly fundin c. Find E(x). d. What is P(0.5 < X <1.5)?S o与 o.s =| 0,2363

Answer 1

a)

for above to be valid: $\int_{0}^{2}$ f(x) dx =1

$\int_{0}^{2}$ f(x) dx = $\int_{0}^{2}$ cx⁴ dx = cx⁵/5|²₀ =c*32/5 =1

c=5/32 =0.15625

b) P(X=1) =0  

c)E(X) = $\int_{0}^{2}$ xf(x) dx = $\int_{0}^{2}$ 0.15625x⁵ dx = 0.15625*x⁶/6|²₀ =0.15625*64/6 =1.6667

d)

P(0.5<X<1.5)= $\int_{0.5}^{1.5}$ f(x) dx = $\int_{0.5}^{1.5}$ 0.15625x⁴ dx = 0.15625 x⁵/5|^1.5_0.5 =0.2363