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6. The bulge size, X, of a Martian ice dome has density function: : f(x)= 20x(5-x)³ for 0 ≤ x ≤ 5 and 0 otherwise. 3125 a) What is the probability that X > 2? b) What is the probability that X < 2? c) What is the probability that 2.1 < X < 4.7?

6. The bulge size, X, of a Martian ice dome has density function: : f(x)= 20x(5-x)³ for 0 ≤ x ≤ 5 and 0 otherwise. 3125 a) What is the probability that X > 2? b) What is the probability that X < 2? c) What is the probability that 2.1 < X < 4.7?

Calculus For The Life Sciences
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
Section13.3: Special Probability Density Functions
Problem 6E
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6. The bulge size, X, of a Martian ice dome has density function:: f(x)= 20x(5-x)³ for 0≤ x ≤ 5 and 0 otherwise. 3125 a) What is the probability that X > 2? b) What is the probability that X < 2? c) What is the probability that 2.1 < X < 4.7? d) What is the expected value of X (E(X))? e) What is the expected value of X - 3? f) What is the expected value of 6X? g) What is the expected value of X² ? h) What is the probability that X is greater than its expected value? i) What is the expected value of X³-3X+1 ? j) What is the 55th percentile of X? k) What is the probability that X is within 0.4 of its expected value? 1) What is the probability that X = 2?
Transcribed Image Text:6. The bulge size, X, of a Martian ice dome has density function:: f(x)= 20x(5-x)³ for 0≤ x ≤ 5 and 0 otherwise. 3125 a) What is the probability that X > 2? b) What is the probability that X < 2? c) What is the probability that 2.1 < X < 4.7? d) What is the expected value of X (E(X))? e) What is the expected value of X - 3? f) What is the expected value of 6X? g) What is the expected value of X² ? h) What is the probability that X is greater than its expected value? i) What is the expected value of X³-3X+1 ? j) What is the 55th percentile of X? k) What is the probability that X is within 0.4 of its expected value? 1) What is the probability that X = 2?
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The bulge size, X, of a Martian ice dome has density function: : for 0 ≤ x ≤ 5 and 0 otherwise. f(x)= 20x(5-x)³ 3125 a) What is the probability that X > 2? .3370 b) What is the probability that X < 2? .6630 c) What is the probability that 2.1 < X < 4.7? .3035 d) What is the expected value of X (E(X))? e) What is the expected value of X - 3? f) What is the expected value of 6X? g) What is the expected value of x²? h) What is the probability that X is greater than its expected value? i) What is the expected value of X³-3X+1 ? j) What is the 55th percentile of X? k) What is the probability that X is within 0.4 of its expected value? 1) What is the probability that X = 2?
Transcribed Image Text:The bulge size, X, of a Martian ice dome has density function: : for 0 ≤ x ≤ 5 and 0 otherwise. f(x)= 20x(5-x)³ 3125 a) What is the probability that X > 2? .3370 b) What is the probability that X < 2? .6630 c) What is the probability that 2.1 < X < 4.7? .3035 d) What is the expected value of X (E(X))? e) What is the expected value of X - 3? f) What is the expected value of 6X? g) What is the expected value of x²? h) What is the probability that X is greater than its expected value? i) What is the expected value of X³-3X+1 ? j) What is the 55th percentile of X? k) What is the probability that X is within 0.4 of its expected value? 1) What is the probability that X = 2?
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