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Consider an urn that contains 10 tickets, labelled $\{ 1 , 1 , 1 , 1 , 2 , 5 , 5 , 10 , 10 , 10 \}$ . From this urn, I propose to draw a ticket. Let X denote the value of the ticket I draw. Determine each of the following:

(a) The probability mass function of X

(b) The cumulative distribution function of X

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    what difficulty do you face in dealing with this question? – 2017-01-28
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    just want to check whether am i correct or wrong – 2017-01-28
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    you might want to show us your working so that someone can check with you? the common practice here is to show your efforts and thoughts. that way others can help you improve and get unstucked. very few people come here to do homework for others. – 2017-01-28

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Let X denote the value of the number on the ticket you draw, then we have a chance of 4 out of 10 to draw a ticket with 1 on it, 1 out of 10 for a ticket with 2, 2 out of 10 for a ticket with 5 en 3 out of 10 for a ticket with 10. Denoted more mathematcally we have $P (X = 1) = 4/10$ and so on. This gives the probability mass function. In order to determine the cummulative distribution, you have to compute the chances $P(X \leq 1), P(X \leq 2), ... , P(X \leq 10)$. However, you will find out that you can reduce this work to 4 computations. Do you see which ones?

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    The pdf is determined by the chances to draw a number, i.e. the chances P(X = x) – 2017-01-28
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    Where 'x' is a possible outcome, so in this case x is in the set {1,2,5,10} – 2017-01-28
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    Sorry, I meant: What about the **cdf**? – 2017-01-28
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    Well, that is what i wrote in my last lines: you compute the chances $P(X \leq x)$ for x going from 1 to 10. But since there are only 4 possible outcomes you only have to compute 4 of these chances – 2017-01-28