Let x be the random variable representing the number of calls received in an hour by a 911 emergency service. a portion of the probability distribution of x is given below. value of x 0 1 2 3 4 probability p(x) 0.25 0.10 0.05 suppose the probability that x = 1 and the probability that x = 2 are the same. what are these probabilities? what is the expected number of 911 calls in an hour?

For any distribution, the sum of the probabilities of all possible outcomes must be 1. In this case, we have to have

We're told that , and we're given other probabilities, so we have

The expected number of calls would be

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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