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Q.4 The probability density function for a continuous random variable X is 2 x; 0 ≤ x ≤K, 21 fx(x) = = 2 (6x) K < x < 6, 15 0 e. w. (i) Find constants K a so that it is a probability density function. (ii) Find cumulative distribution function (cdf), moment generating function (mgf). (iii) Using mgf, find ẞ₁ and ẞ2 and comment on it. (iv) Using cdf find P(2≤ x ≤ 5.5).

Q.4 The probability density function for a continuous random variable X is 2 x; 0 ≤ x ≤K, 21 fx(x) = = 2 (6x) K < x < 6, 15 0 e. w. (i) Find constants K a so that it is a probability density function. (ii) Find cumulative distribution function (cdf), moment generating function (mgf). (iii) Using mgf, find ẞ₁ and ẞ2 and comment on it. (iv) Using cdf find P(2≤ x ≤ 5.5).

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.CR: Chapter 13 Review
Problem 29CR
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Q.4 The probability density function for a continuous random variable X is 2 x; 0 ≤ x ≤K, 21 fx(x) = = 2 (6x) K < x < 6, 15 0 e. w. (i) Find constants K a so that it is a probability density function. (ii) Find cumulative distribution function (cdf), moment generating function (mgf). (iii) Using mgf, find ẞ₁ and ẞ2 and comment on it. (iv) Using cdf find P(2≤ x ≤ 5.5).
Transcribed Image Text:Q.4 The probability density function for a continuous random variable X is 2 x; 0 ≤ x ≤K, 21 fx(x) = = 2 (6x) K < x < 6, 15 0 e. w. (i) Find constants K a so that it is a probability density function. (ii) Find cumulative distribution function (cdf), moment generating function (mgf). (iii) Using mgf, find ẞ₁ and ẞ2 and comment on it. (iv) Using cdf find P(2≤ x ≤ 5.5).
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