Let X and Y are independent and both have exponential distribution,Find ??(?) , if Z=X+Y. Where PDF of X and Y are given as,??(?) = ??−???(?) and ??(?) = ??−???(?). 3. Let X and Y are independent and both have exponential distribution,Find fz(z), if Z=X+Y. Where PDF of X and Y are given as,fx(x) = ae-axu(x) and fy(y) = be-byu(y).

We know, X~ExpaY~ExpbZ=X+Y Therefore, fXx=a.e-axu(x)fYy=b.e-byu(y)

Answered: Let X and Y are independent and both…

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.

Chapter3: The Derivative

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Let X and Y are independent and both have exponential distribution,
Find ??(?) , if Z=X+Y. Where PDF of X and Y are given as,
??(?) = ??−???(?) and ??(?) = ??−???(?).

3. Let X and Y are independent and both have exponential distribution,
Find fz(z), if Z=X+Y. Where PDF of X and Y are given as,
fx(x) = ae-axu(x) and fy(y) = be-byu(y).

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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