Reputation: 25
How to solve the following problem, not quite sure how to do it, using the MATLAB functions: binocdf
, normcdf
, expcdf
:
This is given:
X1 ∈ Bin(10, 0.3), X2 ∈ N(5, 3), X3 ∈ Exp(7)
k = 1, 2, 3
What is this probability P(3 < Xk ≤ 4) = ?
I know that the cumulative distribution function gives you the probability of a stochastic variable of being less than or equal to the input if you use for example:
binocdf(4,10,0.3) = P(X1 ≤ 4)
But how do I use these functions when it's Xk > 3
?
Upvotes: 0
Views: 387
Reputation: 104575
If you remember the properties of a CDF, you can find the probability of an event of a random variable spanned by an interval [a,b]
by simply substituting each end point into the CDF and subtracting the two quantities. Concretely, given f
being the PDF and F
being the CDF of a random variable X
, calculating the probability of the event occurring P(a < X <= b)
is such that:
Source: Wikipedia
Therefore, to compute P(3 < X1 <= 4)
as for your example, do:
out = binocdf(4,10,0.3) - binocdf(3,10,0.3);
I'll leave it to you to figure out the other ones.
Upvotes: 2