Statistics question help
Q1. – A pair of dice is tossed repeatedly. What is the least number of tosses needed so that probability of getting 11 will be greater than
i) 0.5
ii) 0.95
Q2. – A & B play a game in which they alternatively toss a pair of dice. The one who is the first to get a total of 7 wins the game. Find the probability that
i) the one who tosses first will win the game
ii) the one who tosses second will win the game
iii) the game will end up in a tie
Q3 – Concentric circles of radius 1, and 3 inches are drawn on a circular target of radius 5 inches. A man receives 10, 5 or 3 points according to if he hits the target inside smaller circle, inside the middle annular region or inside the outer annular region respectively. Suppose the man hits the target with probability ½, and then is just at random on the circle. Find the expected number of points he will score.
Q4 – If two cards are selected at random from a box which contains 5 cards numbered 1, 1, 2, 2 and 3. Let X be the sum of two numbers and Y denotes the maximum find E(X), E(Y) & E(XY)
Q5 – The probability is 0.02% that an item produced by a factory is defective. A shipment of 10,000 items is sent to its warehouse. Find the probability that at most two products are defective.
Q6 – a die is “loaded” so that the face 6 appears 30% of the times, the opposite face 1 appears 10% of the times, and each of the other faces appear 15% of the times. A die is tossed 6 times. Find the probability that
i) Each face appears once
ii) Faces 4, 5 & 6 each appears twice
Q7 – Among 10,000 random digits, find the probability that the digit 3 appears at most 950 times
Q8 – Suppose f(X) = c1e-2x for x > 0 and g(y) = c2e-3y for y > 0. If X & Y are independent random variables, Find
i) Constants c1 & c2
ii) P[X + Y > 1]
iii) P[X < 2, Y > 1]
Q9 – The joint density function of the random variables X & Y is given by
f(x, y) = 8xy for 0 < y < x < 1 and 0 otherwise.
Find f(x|y) and g(y|x) (i.e. X given Y and Y given X)
Q10 –Suppose that the joint probability density function of random variables X & Y is given by
f(x, y) = cxy for 0 < y < x < 2 and 0 otherwise.
Determine if X & Y are independent
give an example of and addition problem in which you would and would not group the addends differently to add ?
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