1 answer

Suppose F(t) /6 for 0 < t < 6 is the c.df. Y. If Y is...

Question:

Suppose F(t) /6 for 0 < t < 6 is the c.df. Y. If Y is a continuous-type r.v., give the p.d.f. of Y. If Y is a discrete-type r.v., give the p.m.f. of Y. Otherwise, say that Y is none of the above. of a randorm variable

Suppose F(t) /6 for 0 < t < 6 is the c.df. Y. If Y is a continuous-type r.v., give the p.d.f. of Y. If Y is a discrete-type r.v., give the p.m.f. of Y. Otherwise, say that Y is none of the above. of a randorm variable

Answers

F(t) = [t]/6 for 0<=t<=6  

Here [t] represents the greatest integer function

F(y) = [y]/6 for 0<=y<=6 is the cdf of random variable Y.

Since here y can take any values between 0 and 6, therefore Y is a continous type random variable.

Now the pdf of Y

f(y) =\frac{d(F(y)}{dy}

f(y) =\frac{d([y]/6)}{dy}

f(y) = 1/6 when 1<=y<=6

0 otherwise

This is the required pdf of Y.

Please upvote. Thanks!

.

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