excess Ex(x) 3. A box contains lotto cards: 20 cards are with letters, 5 are with...
3. A box contains lotto cards: 20 cards are with letters, 5 are with numbers, and 15 are with pictures. We have taken 2 cards from the box. What are probabilities that we have taken a) 2 cards with pictures c) card with letter and card with number b) at least one card with picture d) no cards with numbers
Examination in probability theory and statistics Variant 9 1. Discrete distribution for X is given by the following table: Probability p ValueX Find distribution function fa) and median Me(0). Calculate mathematical expectation (the mean) M(x), 0.3 -10 0.4 10 0.2 20 0.1 40 variance (dispersion) Da, standard error ơ(X), asymmetry coefficient As(X) and excess Ex(X). 2. Calculate multiplier k. Find mode Mots, median Me(o), mathematical expectation (the mean) Mc) variance (dispersion) D(x) and standard error σ(x) for continuous distributions having...
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excess Ex) 3. A box contains 15 red balls, 10 blue balls, and 5 white balls. We have taken 2 balls from the box. What are probabilities that we have taken c) one red ball and one blue ball a) 2 white balls b) at least one white ball d) no one blue ball
14. A box contains 4 red (numbers from 1 to 4) and 6 blue cards (numbered from 5 to 10). A card is chosen randomly. What is the probability that the card is red given that it is even numbered? a 1/2 b. 1/4 c. 3/4 d. 3/5 e. 2/5 f. None of the above 15. A card is drawn from a well shuffled deck and a second card is drawn without replacement. If the first card is a heart,...
3. A box contains 10 red balls, 6 blue balls, and 4 white balls. We have taken 2 balls from the box. What are probabilities that we have taken c) one red ball and one white ball b) at least one blue bal a) 2 blue balls d) no one red ball
A box contains four cards, each card marked with a number. The numbers are "1", "2", "4", "6". A chance process consists of drawing three cards from the box, one after the other without replacement and computing the value of the range of the three numbers. The range is the largest number minus the smallest number. To illustrate, if the cards drawn are "1", "4", and "2" the outcome will be 4 - 1 = 3, if "2", "4", and...
3. Two boxes each contain three cards. The first box contains cards labelled-1,1 and 2; the second box contains cards labelled-2, -1 and 2. In a game, a player draws one card at random from each box and his score, W, is the product of the numbers on the two cards. w -4 -1 N 4 P(W =w) 1 9 3 9 1 1 9 a) Complete the above table. (4 marks) b) Find P(-2 SW 52). (2 marks) c)...
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Homework in probability theory Variant 1 A box contains 15 red balls, 10 blue balls, and 5 white balls. 1. 2 balls are taken from the box. Consider the following events: A) the first ball is red B) the first ball is blue C) the first ball is white Find the following probabilities a) p(A)-? D) the second ball is red E) the second ball is blue F) the second ball is white b)...
1. We roll two fair 6-sided dice. Compute the probabilities of the following events. (a) The sum is at most 6. (b) The sum is more than 6. (c) The sum is at most 6 and at least one die is a 4. 2. Consider the letters a,b,c. Suppose we draw 2 of the letters at random (allowing for repetition). Assume order matters. That is, ab is not the same as ba: Let A : The 2 letters are distinct....
5. This is a bonus question. You will get extra marks for doing it. Four probabilists are playing a game of cards. Each of them has been dealt a hand of 13 cards from a standard wel shuffled pack of 52 cards. Note that there are 12 pictures cards namely the Jack, Queen and King of each of the four suits (Clubs, Diamonds, Hearts and Spades). Suppose that one of the probabilists is picked uniformly at random. (a) What is...