4. A box contains N identical balls numbered 1 through N. Of these balls, n are...
1.23 A box contains n identical balls numbered 1 through n [Papoulis 1.1]. Suppose k balls are drawn in succession. a) what is the probability that m is the largest number drawn? b) what is the provability that the largest number drawn is less than or equal to m?
Box 1 contains a red balls and b white balls. Box 2 contains c red balls and d white balls. One ball is randomly drawn from Box 1 and put into Box 2, and then one ball is randomly drawn from Box 2 and put back in Box 1. Finally, one ball is drawn at random again from Box 2. Let X denote the number of red balls drawn from Box 2 the 2nd time. Write down the distribution of...
Question 29 (4 points) Two boxes each contain five numbered balls: • Box 1 contains balls with numbers 3, 3, 3, 4, 5 • Box 2 contains balls with numbers 1, 1, 2, 2, 2 (a) You will randomly select one ball from each box. Let X be the difference between the numbers selected from the first and second box. Find the probability distribution of X. You can simply list the probabilities for each possible value of X instead of...
1.3-9. An urn contains four balls numbered 1 through 4. The balls are selected one at a time without replacement. A match occurs if the ball numbered m is the mth ball selected. Let the event Ai denote a match on the ith draw, i = 1, 2, 3, 4. (a) Show that PIA)for each i. 3! 4 (b) Show that P(AMA) =-, i 치. 4!
1.3-9. An urn contains four balls numbered 1 through 4 The balls are selected one at a time without replacement. A match occurs if the ball numbered m is the mth ball selected. Let the event A, denote a match on the ith draw i 1,2, 3, 4. 3! (a) Show that P(A)for each i 4! 2! (b) Show that P(A, nA,) =-, i 1! (d) Show that the probability of at least one match is (e) Extend this exercise...
2. A box contains 4 white and 6 black balls. A random sample of size 4 is chosen. Let X denote the number of white balls in the sample. An additional ball is now selected from the remaining 6 balls in the box. Let Y equal 1 if this ball is white and 0 if it is black. Find (a) Var(Y|X=0). (b) Var(X)Y= 1).
An urn contains balls numbered 1 through 6. Balls are repeatedly selected one at a time and with replacement. Let Xz be the number of the selection on which the first 3 appears, and let X4 be the number of the selection on which the first 4 appears. Let Px. y. (x3|x4) be the conditional distribution of X3, given that X4 = x4. (a) Find Px, x,(5|3) (b) Find Px, x,(315)
Problem #4: (10 points) In a state lottery, the player picks 6 numbers from a sequence of 1 through 51. At a lottery drawing, 6 balls are drawn at random from a box containing 51 balls, numbered 1 through 51. Find the following. (a) Probability the player matches exactly 5 numbers (b) Probability the player matches all 6 numbers (i.e. wins the lottery!) Problem #4: (10 points) In a state lottery, the player picks 6 numbers from a sequence of...
An urn contains 5 balls numbered 1 to 5. Two balls are drawn replacement Let X be the sum of the two numbers drawn. (a). What are the possible values of X? (b). if let X be the subtraction of the two numbers drawn.What are the possible values of X? (c). if let X be the product of the two numbers drawn.What are the possible values of X? (d). if let X be the Quotient of the two numbers drawn.What...
L. An un contains n red balls and n black balls. Balls are drawn sequentially from the urn one at a time withont replacement. Let the first black ball is chosen. Find EX X denote the number of red balls removed befor