Hello So the answer to this question can be found on chegg b

Hello, So the answer to this question can be found on chegg, but I just don\'t understand how they where to find the CDF from the PMF. Can someone please do a step by step solution and explain their relationships? My text doesn\'t a very good explantion either so I\'m totally lost here. Thank you.

1.5.4. Let px(x) be the pmf of a random variable X. Find the cdf F(x of X and sketch its graph along with that of px(x) if: (a) px (z) = 1, z = 0, zero elsewhere. (b) PX(x)-, x =-1, 0, 1, zero elsewhere. (c) px(z)=x/15, x= 1, 2, 3, 4, 5, zero elsewhere.

Solution

Cumulative function of x is the cumulative probability upto value x

i.e. P(X<=x) is called the cumulative probability and the list is called CDF

For discrete variables it is the sum of prob upto x

and for continuous variables it is the integral value upto x

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a) Px(x) =1, x =0

            =0 otherwise

This is a pdf of a variable x taking single value 0 alone.

Hence Cdf of x is 0, x<0

                          1, x>=1

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b) This is a discrete variable

x         -1      0       1

p               1/3   1/3     1/3

Cum p        1/3    2/3     1

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c) This is again a discrete variable x taking natural numbers 1 to 5

Pdf x       

x            1            2           3             4              5       Total

p           1/15       2/15       3/15        4/15          5/15       1

Cum       1/15      3/15       6/15       10/15          1

prob