Statistics and Probability Answers

(a) During a laboratory experiment the average number of radioactive particles passing through a counter in 1 millisecond is 4. what is the probability that 6 particles enter the counter in a given milliseconds
(b) The height of adult women in the United States is normally distributed with mean 64.5 inches and S.D 2.4 inches. Find the probability that a randomly chosen women is a) less than 63 inches tall b) less than 70 inches tall c) between 63 and 70 inches tall. d) Alice is 72 inches tall. What percentage of women is shorter than Alice

A shipment of 8 similar microcomputers to a retail outlet contains 3 that are defective. If a school makes a random purchase of 2 of these computers, find the probability distribution for the number of defectives? Also, find its mean and standard deviation

(a) The chances that an academician, a business man and a politician becoming Vice Chancellor of a university are 0.5, 0.3 and 0.2 respectively. The probability that research work will be promoted in the university by these 3 gentlemen are respectively are 0.8, 0.6 and 0.4. It is found research work has been promoted by the university. What is the chance that an academician has become the VC?

(b) A can hit a target 3 times in 5 shots; B can hit 2 times in 5 shots; C can hit 3 times in 4 shots. They fire a volley. What is the probability that two shots hit?

Let X denote the temperature ( ) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density function is
f(x, y) =c (4x+2y+1) , . i) Find c, ii) Find the marginal densities for X and Y, iii) Find the probability that on a randomly selected day the air air temperature will exceed
iv) Are X and Y independent?

A ship is fitted with three engines A, B and C. These three engines function independently of each other with probabilities ½ , ¼, ¼ respectively. For ship to be operational atleast two of its engines must function. Let E denote the event that the ship is operational and E1,E2 and E3 denote the events that engines A,B and C are functioning. Then validate the following.
(a). P(E1C / E) = 3/16
(b) P(E / E2) = 5/16
(c) P( Exactly two engines of the ship are functioning / E) = 7/8.

(b) The trouble shooting capability of an IC chip in a circuit is a random variable X whose distribution function is given by where x denote the number of years. Find the probability that the IC chip will work properly (i) less than 8 years (ii) beyond 8 years (iii) between 5 to 7 years (iv) anywhere from 2 to 5 years

A player tosses 3 fair coins. He wins Rs.500 if 3 heads appear, Rs.300 if 2 heads appear, Rs.100 if 1 head occurs. On the other hand, he loses Rs.1500 if 3 tails occur. Find the expected gain of the player and variance.

a fair coin is tossed until for the first time the same result appears twice in succession(i.e until the TT or HH).Describe the sample space and assign probabilities that reflects the fairness of the coin..find the probabilities of the events
A="The coin is tossed at most five time"
B="the total number of tossed is odd'"
C=AUB
D= A(intersection)B

Given the following set of data for a trivariate distribution
Y 6 10 9 14 7 5
X1 1 3 2 -2 3 6
X2 3 -1 4 7 2 -4
(i) Calculate the Multiple regression of Y on X1 and X2
(ii) Predict Y when X1=-1 and X2=4

a fair coin is tossed until , for the first time the same result appears twice in succession describe the sample space assign probabilities that reflect the fairness of the coin find the probabilities?