8. Let X be the r.v. representing time (in hours) for a student to complete an assignment. The pdf of X is Sax² + x, p(x) = [0, 0 ≤ x ≤ 0.5, others. Determine the value of constant a. b) Find the cdf of X. c) Find the probability that a student completes an assignment in 20 minutes. d) Find the probability that a student spends more than 10 minutes to complete an assignment.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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8. Let X be the r.v. representing time (in hours) for a student to complete an
assignment. The pdf of X is
p(x) =
Jax² + x,
10, others.
0 ≤ x ≤ 0.5,
a) Determine the value of constant a.
b) Find the cdf of X.
c) Find the probability that a student completes an assignment in 20
minutes.
d) Find the probability that a student spends more than 10 minutes to
complete an assignment.
Transcribed Image Text:8. Let X be the r.v. representing time (in hours) for a student to complete an assignment. The pdf of X is p(x) = Jax² + x, 10, others. 0 ≤ x ≤ 0.5, a) Determine the value of constant a. b) Find the cdf of X. c) Find the probability that a student completes an assignment in 20 minutes. d) Find the probability that a student spends more than 10 minutes to complete an assignment.
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