Let X be a continuous random variable defined on the interval [0, 4] with probability density function: p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. Also find the probability that X is less than some number a, assuming 0 < a < 4?

Let X be a continuous random variable defined on the interval [0, 4] with probability density function: p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. Also find the probability that X is less than some number a, assuming 0 < a < 4?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 30CR

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Question

Let X be a continuous random variable defined on the interval [0, 4] with probability density function:

p(x) = c(1 + 4x)

(a) Find the value of c such that p(x) is a valid probability density function.

(b) Find the probability that X is greater than 3.

(c) If X is greater than 1, find the probability X is greater than 2. Also find the probability that X is less than some number a, assuming 0 < a < 4?

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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