Question

If X is a uniformly distribution discrete random variable with possible values the integers from -3 to 5(inclusive).
A) What is the probability distribution function for x?
B)What is the probability that X is between 1 and 3 (inclusive)
c) find the expect value of X
d) find the variance of X (just use general computational formula)
e) find the standard Deviation of X.

Answer 1

A) Let r = -3, -2, -1, 0, 1, 2, 3, 4, 5.
\[\large P(X = r)=\frac{1}{5-(-3)+1}=\frac{1}{9}\]

Answer 2

Two ways of doing part (b). Use the CDF (once you find it) or add the appropriate probabilities.

Answer 3

k i guess i will use the cdf

Answer 4

1<=x<=3

Answer 5

It's up to you, but the second method is much less work. Finding the CDF ends up being the same process in the end (if you recall that recent question you asked about finding the CDF of a discrete uniform distribution).

Answer 6

yeah i recall that

Answer 7

i guess the prof doesnt mind about the second way

Answer 8

c) The expected value of X is found from:
\[\large E(X)=\frac{1}{9}(-3-2-1+1+2+3+4+5)=you\ can\ calculate\]

Answer 9

k isee

Answer 10

i guess part b , d and e are left

Answer 11

d)
\[\large Var(X)=\sum_{}^{}x^{2}.\frac{1}{9}-[E(X)]^{2}\ for\ x=-3,-2,.........4,5 \]

Answer 12

i see var(x)=summation (-3)^2*1/9- {E(x)]^2 know rest

Answer 13

Now the last part is e)

Answer 14

e) Take the square root of the variance.

Answer 15

k thx so much @kropot72

Answer 16

You're welcome :)