Question 1: Find the value of c that makes each of the following valid probability density functions. (a) For a > 0, B > 0: Sc.e- for a > « f (x) = с otherwise. (b) f (x) = c · [G(x))* g(x) for x E R, = C• where G(x) and g(x) are the cumulative distribution function and density function (respec- tively) of some other random variable defined on R.

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Q: Is f(x) a legitimate probability mass function? (1 – p)"='p =p+ (1 – p)p + (1 – p)²p+ • …· ² 1 x=1

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Q: 55 Prove that the functio: probability density F Given f(x)= 2(1-x) and (0<x< ضافة ملف

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Q: Question is attached.

A: (a)The value of c can be derived as follows:

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Q: 1 (a) ƒ (kx) = 2x+1_2²²₂ = - 2*, x = 1, 2, ..., N, and zero elsewhere (b) f(x)=p(1-p)*, x=0,1, 2,…

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