all the necessary steps have been shown above. In case of doubt, comment below. And do like, if possible.
6. (5 marks) Suppose Y is a Normal random variable. If P(Y <1)=0.25 and P(Y >...
ULULUI Let Z be a standard normal random variable. What is P(-2.22 <Z<0.25)? 0.2212 0.3488 0.5855 O 0.6902
1. Given that z is a standard normal random variable, compute the following probabilities. a. P(Z < 1.38) b. P(z 2 1.32) c. P(-1.23 Sz5 1.23)
Suppose that the standard normal random variables X and Y are independent. Find P(0 < X<Y). 8 O 1 4T 0 1 8л Ala
3, Let X be a normal random variable with μ (a) If P(Xc)-0.791, what is the value of c? (b) If P(X<c) 0.36, what is the value of c? (c) If P(X>c) 0.40, what is the value of c? 10, and σ=2.
Assume Z is a random variable with a standard normal distribution and c is a positive number. If P(Z > c) = 0.25, then PC – c< < c) = 0.5. O True OFalse Exactly 50% of the area under the normal curve lies to the left of the mean. O True OFalse If X represents a random variable coming from a normal distribution and P(X < 5.2) = 0.5, then P(X > 5.2) = 0.5. O True O False
f(x,y)= 0 1. (15 marks) Suppose X and Y are jointly continuous random variables with probability density function 12, 0<x<1, 0<y<0.5 else a) (5 marks) Find P(X - Y <0.25). b) (5 marks) Find P(XY <0.30). c) (5 marks) Find V (2x - 5Y+30).
6. Let X be a normal random variable with mean u = 10. What is the standard deviation o if it is known that p (IX – 101 <>) =
Suppose Z is a standard normal random variable. (See problem.) If P(-z<z<z) 0.796, find Question 1 Find P(-2.46 <Z<-0.98) Question 2
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
5. Let Z be a standard normal random variable. Use the table on page 848 of the textbook to evaluate the following. (a) P(Z < 0.04) (b) P (0.09 < 20 S 0.81) (c) P(Z <1.3) (d) P(-2 <7 <1) (e) P(Z -0.1) (Z -0.2) (Z -0.3) (Z-0.4) > 0)