A letter is chosen uniformly at random from {A, B, . . . , Z}. If...
A letter is chosen uniformly at random from {A, B, . . . , Z}. If that letter is one of the vowels (i.e. A, E, I, O or U) then a second letter is chosen uniformly at random from {A, B, . . . , Z}. Let L be the number of letters chosen and let V be the number of vowels chosen.
(i) What is the expected value of L?
(ii) What is the expected value of V?
(iii) Are L and V independent?
(iv) What is the probability that two letters are chosen and that they are equal?
(v) What is the probability that at least one U is chosen?
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A letter is chosen uniformly at random from {A, B, . . . , Z}.
If...
[2] [3] (5) (a) A soccer squad contains 3 goalkeepers, 7 defenders, 9 midfielders and 4...
[2] [3] (5) (a) A soccer squad contains 3 goalkeepers, 7 defenders, 9 midfielders and 4 forwards. (i) In how many ways can a team of 1 goalkeeper, 4 defenders, 4 midfielders, and 2 attackers be chosen from this squad? (ii) Two of the defenders refuse to play together. In how many ways can a team be chosen that contains at most one of these two defenders? (b) Let p and q be real numbers. A random variable X has...
Exercise 2.38. We choose one of the words in the following sentence uniformly at random and then choose one of the...
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2. You randomly choose a letter from (A, B, C, D, E and a friend randomly...
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can you try these I do not know if they are correct (from e-h mainly) please...
can you try these I do not know if they are
correct
(from e-h mainly)
please check the others if you have the time to
The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and sometimes y). Suppose we randomly select 8 letters from the alphabet without replacement. Let X = the number of vowels chosen (including y as a vowel). a. How many possible ways are there to select the 8 out of...
1) (a) (14 pts.) Consider the experiment in which a number is chosen uniformly in (1;...
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Let X1, X2, ..., Xn be a random sample of size 5 from a normal population...
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[2] [3] (5) (a) A soccer squad contains 3 goalkeepers, 7 defenders, 9 midfielders and 4 forwards. (i) In how many ways can a team of 1 goalkeeper, 4 defenders, 4 midfielders, and 2 attackers be chosen from this squad? (ii) Two of the defenders refuse to play together. In how many ways can a team be chosen that contains at most one of these two defenders? (b) Let p and q be real numbers. A random variable X has...
Exercise 2.38. We choose one of the words in the following sentence uniformly at random and then choose one of the letters of that word, again uniformly at random: SOME DOGS ARE BROWN (a) Find the probability that the chosen letter is R. (b) Let X denote the length of the chosen word. Determine the probability mass function of X. (c) For each possible value k of X determine the conditional probability P(X k|X 3) Hint. The decomposition idea works...
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can you try these I do not know if they are
correct
(from e-h mainly)
please check the others if you have the time to
The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and sometimes y). Suppose we randomly select 8 letters from the alphabet without replacement. Let X = the number of vowels chosen (including y as a vowel). a. How many possible ways are there to select the 8 out of...
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Problem 3.4 (10 points) Consider this...
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3. A computer chooses 100 independent random numbers, each uniformly from the set of integers between 1 and 200. What is the expected value of: (a) The number of the chosen numbers which are multiples of 10
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