The Student Room Group

probability

so ive been given this question but im really confused about what it wants me to get...

The discrete random variable X is defined on = {0, 1, 2, 5} with
P(X = i) = c(i + 10)2 , c > 0
(a) Calculate c and provide the probability function of X.


any help would be greatful xx

Scroll to see replies

Well you should know that 'i' can only be 0, 1, 2 or 5 and the sum of all P(X = i) is 1.
yeah so do i do p(x=0) + p(x=1) + p(x=2) + p(x=5)=1
which gives.... 590c=1 so c=1/590???

then what does it mean by provide the probability function of X... what does this look like???
"Probability function"? Usually it's P(X <= x)
yeah i just dont know what it would be in this case :/
would it just be P(X<=5) do you think???
You'd have to express it in terms of x (= {0,1,2,5})
so p(0<=X<=5)????
Original post by mickymouse1995
yeah so do i do p(x=0) + p(x=1) + p(x=2) + p(x=5)=1
which gives.... 590c=1 so c=1/590???

then what does it mean by provide the probability function of X... what does this look like???


The probability function (not cumulative prob function) relates a probability to each possible value of x.

So you can either simply put the value of c into the original expression, or draw out a table:

x 0 1 2 5
P(x) .. ...

And put in the individual values for the probs.
but isnt that continuous rather than discrete??? wouldnt it just be like P(X=i)=1/590*(i+10)^2
oops.

so yeah, the probability mass function is what you're trying to find, and it looks like a table
thank you :smile: i understand now xx
so now i have too do the following...
(b) Derive the distribution function of the discrete random variable X.

is the distribution function F(x) how do you calculate that... is that by integration/????
ok that's the cumulative function P(X<=x), you probably have to do that in the form of a table as well
even though its still discrete??? what do i need for the table???
x 0 1 2 5
P(X<=x) .. ...
so do i need to integrate then????
or am i just being really dumb/??
It's a discete r.v., no calculus required
ok so i literally add up the probabilities???

Quick Reply