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4. Let f(x) = xe¯* if x > 0 and f(x) = 0 if x < 0. (a) Verify that f is a probability density function. (b) Find P(1 < X < 2). %3D 6. Let f(x) = kx²(1 – x) if 0 < x < 1 and f(x) = 0 if x <0 or x > 1. (a) For what value of k is ƒ a probability density function? (b) For that value of k, find P(X >;). (c) Find the mean.

4. Let f(x) = xe¯* if x > 0 and f(x) = 0 if x < 0. (a) Verify that f is a probability density function. (b) Find P(1 < X < 2). %3D 6. Let f(x) = kx²(1 – x) if 0 < x < 1 and f(x) = 0 if x <0 or x > 1. (a) For what value of k is ƒ a probability density function? (b) For that value of k, find P(X >;). (c) Find the mean.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9-10 Sketch a direction field for the differential equation. Then use 10. y' = x – y + 1 it to sketch three solution curves. 2. Verify that y= -t cos t – t is a solution of the initial-value problem dy t = y + t²sin t dt y(7) = 0 4. (a) For what values of k does the function y = cos kt satisfy the differential equation 4y" = –25y? (b) For those values of k, verify that every member of the family of functions y = A sin kt + B cos kt is also a 7.1:4 solution.
Transcribed Image Text:9-10 Sketch a direction field for the differential equation. Then use 10. y' = x – y + 1 it to sketch three solution curves. 2. Verify that y= -t cos t – t is a solution of the initial-value problem dy t = y + t²sin t dt y(7) = 0 4. (a) For what values of k does the function y = cos kt satisfy the differential equation 4y" = –25y? (b) For those values of k, verify that every member of the family of functions y = A sin kt + B cos kt is also a 7.1:4 solution.
4. Let f(x) = xe¯* if x > 0 and f(x) = 0 if x < 0. (a) Verify that f is a probability density function. (b) Find P(1 < X < 2). %3| 6.8: 4 6. Let f(x) = kx²(1 – x) if 0 < x < 1 and f(x) = 0 if x < 0 %3D or x > 1. (a) For what value of k is f a probability density function? (b) For that value of k, find P(X > ;). (c) Find the mean. 6.8:6
Transcribed Image Text:4. Let f(x) = xe¯* if x > 0 and f(x) = 0 if x < 0. (a) Verify that f is a probability density function. (b) Find P(1 < X < 2). %3| 6.8: 4 6. Let f(x) = kx²(1 – x) if 0 < x < 1 and f(x) = 0 if x < 0 %3D or x > 1. (a) For what value of k is f a probability density function? (b) For that value of k, find P(X > ;). (c) Find the mean. 6.8:6
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