Consider the card experiment of dealing a card from a...

Consider the card experiment of dealing a card from a standard deck. Suppose that we assign a value to each card as follows: an ace has value 2, a face card has value 10, and otherwise the value of a card is the number of the card. Let X denote the value of the card. (a) (1 point) Write the probability density and cumulative distributional functions of X. (b) (1 point) Draw probability density function. (c) (1 point) Find the mean and median of X.

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00:01 Hello, let's have a look on the question.

00:02 So here x denotes the value of card.

00:06 So for a part, we can find out pdf and cdf for different values.

00:14 So pdf here will be f of x is equal to.

00:17 This will be for x equal to 2.

00:20 For x equal to 2, we have 2 upon 13.

00:23 For x equal to 3, 1 upon 13.

00:26 X equal to 4, we have 1 upon 13.

00:29 X equal to 5 is 1 upon 13 x upon 6 x equal to 6 is 1 upon 13 next we have x equal to 7 again 1 upon 13 x equal to 8 is also 1 upon 13 and x equal to 9 is 1 upon 13 and x equal to 10 is 4 upon 13 so this is the pdf next we need to find out the cdf so cdf for this would be cdf here is this was small f of x and it is represented by capital f of x.

01:09 So this will be equal to 2 by 13 when x is between 2 to 3.

01:17 Next we have 3 by 13 when x is between 4 to 5.

01:24 5 by 13 when x is between 5 and 6.

01:31 Next we have 6 by 13 when x is between 6 and 7.

01:35 Next value is 7 by 13 when the value of x is between 7 to 8.

01:42 Next value is 8 by 13.

01:45 8 by 13 when x is between 8 and 9.

01:50 Next we have 9 by 13 when x is between 9 and 10 and 1 when x is between 10 to infinity.

02:01 So this is the cdf function and pdf function...