Statistics - Discrete Random Variables- probablility

1.Thirty per cent of all patients undergoing a particular diagnostic procedure require a sedative. In a random sample of 10 patients undergoing the procedure, what is the probability that
a.at least half will require a sedative?
b.fewer then 3 will require a sedative?
c.at least 9 will not require a sedative?

2.The duration of human pregnancies from conception to birth is approximately normally distributed, with a mean of 265 days and a standard deviation of 15 days.
a.What is the probability that the duration of human pregnancy is less than or equal to 228 days?
b.What is the probability that the duration of a human pregnancy exceeds 300 days?
c.What is the probability that the duration of a human pregnancy lasts from 238 days to 299 days?
d.Twenty percent of human pregnancies last more than what amount of time?

3.An airline company knows that 8% of its passengers will not show up for their scheduled flights. A plane has 175 seats.
a.What is the probability that 10 passengers or fewer will not show up?
b.What is the probability that from 10 to 15 passengers will not show up?
c.What is the probability that exactly 10 passengers will not show up?
d.What is the probability that more than 19 passengers will not show up?

Please choose the correct answer and write briefly why.
A property of continuous distributions is that:
a. As with discreterandom variables, the probability distribution can be approximated by a smooth curve
b. Probabilities for continuous variables can be approximated using discreterandom variables
c. Unlike discret

Please help with the following problems.
1. Describe the correlation in this graph (see graph in attachment)
2. Which of these is true for the correlation coefficient?
- its range is [-1 1]
- we use r to represent it
- we use r^2 to represent it
- both 1 and 2
- both 1 and 3
3. Indicate whether the random variabl

Let four random variables X1, X2, X3, X4 have common mean m1=m2=m3=m4= 5 and common variance (sigma 1)^2= (sigma 2)^2= (sigma 3)^2= (sigma4)^2= 6 and common correlation coefficient p(sub ij)= .1, i does not equal j. Determine the mean and the variance of Y=X1 +X2 + X3 + X4

Let F(x)=....
(a) Show that F(x) is a distributiion function of a discrete random variable.
(b) Find the corresponding PMF.
Let X have a distribition function F(x) = (1 - 2^-x)I[0,oo)(x). Define the following events:
A = {X > 1)
B = {X >2) U {X 3) U {X 5

1. A coin is tossed 3 times. Discreterandom variable X is equal to the number of times Heads comes up. Discreterandom variable Y has the value 1 if the first toss comes up heads and 0 otherwise.
(a) Find Pr[(X=1)n(y=1)]
Are X and Y independent random variables?

1. If you could stop time and live forever in good health, what age would you pick? Answers to this question were reported in a USA Today Snapshot. The average ideal age for each age group is listed in the following table; the average ideal age for all adults was found to be 41. Interestingly, those younger than 30 years want to