1.Find the value of the constant, k, such that the function is a probability density function on the indicated interval.

f(x)=k squareroot of x ; [0,1]

2.F is a probability density function for the random variable X defined on the given interval. Find the indicated probabilities.

f(x)=1/12x ; [1,5]

P(2

P(1

P(x>3)

P(x=5)

3.Find the mean, variance and standard deviation of the random variable x associated with the probability density function over the indicated interval.

f(x)=30(x^4 -x^5) ; [0,1]

mean=

variance=

standard deviation=

4.On the average, a student takes 75 wo/min midway through an advanced court reporting course. Assuming that the dictation speeds of the students are normally distributed and that the standard deviation is 20 wo/min, what is the probability that a student randomly selected from the course can take dictation at the following speeds?

More than 87 wo/min?

between 63 and 89 wo/min?

less than 60 wo/min?