Suppose a random variable has the following distribution
X= -3 -1 0 2 3 5 8
PR 0.21 0.18 0.06 0.12 0.20 0.08 0.15
(imagine a table)
Find its mean, standard deviation, skewness and kurtosis. Also, the prob- ability that X1 + X2 +
X3 > 12, where X1, X2 and X3 are independent random variables, all having the same (above)
distribution.
Solution
mean=m= -3 * 0.21 + -1 * 0.18 + 0 *0.06 + ... variance = (-3-m)^2 * 0.21 + (-1-
m)^2 * 0.18 + .... std= sqrt(variance) Similarly you can calculate the skewness and kurtosis
formulas are given here: http://en.wikipedia.org/wiki/Skewness For getting the probality of
X1+X2+X3>12, you need to list out all such possibilities (8,8,8) : prob = 0.15*0.15*0.15 (8,8,5):
prob=0.15*0.15* 0.08 etc.. There are not many cases If you don\'t want to do this, you can use
the moment generating functions, but that becomes tedious because the distribution is not a
standard one..
Suppose a random variable has the following distributionX= -3 -1 0.pdf
1. Suppose a random variable has the following distribution
X= -3 -1 0 2 3 5 8
PR 0.21 0.18 0.06 0.12 0.20 0.08 0.15
(imagine a table)
Find its mean, standard deviation, skewness and kurtosis. Also, the prob- ability that X1 + X2 +
X3 > 12, where X1, X2 and X3 are independent random variables, all having the same (above)
distribution.
Solution
mean=m= -3 * 0.21 + -1 * 0.18 + 0 *0.06 + ... variance = (-3-m)^2 * 0.21 + (-1-
m)^2 * 0.18 + .... std= sqrt(variance) Similarly you can calculate the skewness and kurtosis
formulas are given here: http://en.wikipedia.org/wiki/Skewness For getting the probality of
X1+X2+X3>12, you need to list out all such possibilities (8,8,8) : prob = 0.15*0.15*0.15 (8,8,5):
prob=0.15*0.15* 0.08 etc.. There are not many cases If you don't want to do this, you can use
the moment generating functions, but that becomes tedious because the distribution is not a
standard one.
