Suppose X ~ normal(mean=5, SD=3). Calculate the following. (Try these both using R and a table.)
Pr(X < 6)
Pr(X > 0)
Pr(0 < X < 5)
Pr(2 < X < 8)
Pr(|X - 5| > 2)
Suppose Y ~ normal(mean=200, SD=18). Calculate the following. (Again, try these both using R and a table.)
Pr(Y > 250)
Pr(180 < Y < 220)
Pr(|Y - 180| > 20)
[problem 6.3 in Sokal & Rohlf, pg 125] Assume that the petal length of a population of plants of species X is normally distributed with mean=3.2cm and SD=0.8cm. What proportion of the population would be expected to have a petal length:
Greater than 4.5cm?
Greater than 1.78cm?
Between 2.9 and 3.6cm?
Suppose X and Y are independent, X ~ binomial(n=5, p=0.1), and Y ~ binomial(n=5, p=0.4). Calculate the following.
E(X+Y)
SD(X+Y)
E[(X+Y)/2]
SD[(X+Y)/2]
E(X - Y)
SD(X - Y)
Suppose X1, X2, X3, ..., X10 are independent and identically distributed (iid), with mean=3 and SD=3. Calculate the following.
E(X1 + X2 + ... + X10)
SD(X1 + X2 + ... + X10)
E[(X1 + X2 + ... + X10)/10]
SD[(X1 + X2 + ... + X10)/10]
Last modified: Wed Feb 22 09:44:03 EST 2006 |