Thirteen cards numbered 1,...,13 are shuffled and dealt one at a time. Say a match occurs on deal k if the kth card revealed is card number k. Let N be the total number of matches that occur in the thirteen cards. Determine E[N].

E[N] = 1

Step-by-step explanation:

Here is the hint we are given on this problem - " Write N = + + · · · + where is the event that a match occurs on deal k. "

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Now the standard thing is to do is let = 1, if there is a match on the -th pick and 0 otherwise. The number of matches is given to be + . . . + . Knowing that, we can use the linearity of expectation -

There are 13 cards and for -th pick, the probability of having a card with number is 1 / 13. Therefore, E[N] = E[ + . . . + ] = 1

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Solution: E[N] = 1

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0