andom variable X has CDF given as follows. Find the PMF of X. Find the PMF of X, and confirm that it is a valid PMF.

Complete Question

Random variable X has CDF given as follows

Find the PMF of X.Find the PMF of X, and confirm that it is a valid PMF.  

Generally the PMF is

      X               0        1       2      3         4       5  

    P(X = x)                                    

Generally to prove the validity of the PMF we add the probabilities , if it is equal to  1 then the PMF is valid otherwise , the PMF is not valid

So

Hence the PMF is valid

Step-by-step explanation:

Generally the probability of  X = 0  is evaluated as

=>    

=>    

Generally the probability of  X = 1  is evaluated as

=>    

=>    

Generally the probability of  X = 2  is evaluated as

=>    

=>    

Generally the probability of  X = 3  is evaluated as

=>    

=>    

Generally the probability of  X = 4  is evaluated as

=>    

=>    

Generally the probability of  X = 5  is evaluated as

=>    

=>    

Generally the PMF is

      X               0        1       2      3         4       5  

    P(X = x)                                    

Generally to prove the validity of the PMF we add the probabilities , if it is equal to  1 then the PMF is valid otherwise , the PMF is not valid

So

Hence the PMF is valid

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step-by-step explanation:

∠cbe and ∠deb are same-side interior angles.

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