Let y denote a geometric random variable with probability of success p. a show that for a positive integer a, p(y > a) = qa . b show that for positive integers a and b, p(y > a + b|y > a) = qb = p(y > b). this result implies that, for example, p(y > 7|y > 2) = p(y > 5). why do you think this property is called the memoryless property of the geometric distribution? c in the development of the distribution of the geometric random variable, we assumed that the experiment consisted of conducting identical and independent trials until the first success was observed. in light of these assumptions, why is the result in part (b) "obvious"?

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

4 puzzles in 3 hours

step-by-step explanation: