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![5. Let U and V be independent random variables, with the probability density functions
√³t² 0≤ t ≤2
{$²
Find Pr[U ≤ V].
fu(s) =
1 s≥1
s²
otherwise
fv(t) =
0 otherwise](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd3c2ff7-376d-42ab-9375-076cf278b626%2F970c9658-d4a7-43d8-98b9-2da54220678f%2F72qhxq8_processed.png&w=3840&q=75)
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- Show that each function defined as follows is a probability density function on the given interval; then find the indicated probabilities. f(x)=(1/2)ex/2;[0,) a. P(0X1) b. P(1X3) c. P(X2)Show that each function defined as follows is a probability density function on the given interval; then the indicated probabilities. f(x)=12(1+x)3/2;[0,) a. P(0X2) b. P(1X3) c. P(X5)