Q1:

print(integrate(function(t) t^4 * dnorm(t), -Inf,Inf))  # about 3

# or, note that Z^2 has a chi-squared distribution with 1 degree of
# freedom, and use the information in Sec. 7.33

Q2:

expMdn <- function(lambda) 
{
   qexp(0.5,lambda)
}

print(expMdn(2.5))  # about 0.28

Q3:

r43 <- function(n) 
{
   (runif(n))^0.25
}

print(mean(r43(10000)))  # about 0.8 

Q4:

n <- rnorm(10000,28.8,3.1) 
n25 <- n[n >= 25]
mean(n25)

Q5:

# need P(N(552) <= 4) 
# N(552) is Poisson with param 552 x (1/100) = 5.52
print(ppois(4,5.52))