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- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BProve that I(X; Y |Z) ≥ I(X; Y ) . Note: X, Y, and Z are random variables. X and Z are independent.Suppose for an international football tournament, you wish to find the probability of the country who can win the final game. You can find the odds for winning from your local bookie [A bookie sets odds, accepts and places bets, and pays out winnings on behalf of other people]. Odds are mathematically treated as a fraction. If the odds for the Morocco vs Argentina game are 5 to 1, the fraction is 1 / 5. So to convert the fraction into probability of winning, take the numerator and divide it by the denominator plus 1. Use the Frac.class in Java to help you convert any given odds into probability. Display your result as a percentage on you console.
- This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".Q1/ The ideal gas equation of state is given by: PV = nRT Where: P is the pressure (atm), V is the volume (L), T is the temperature (K), R=0.08206 (L atm)/(mol K) is the gas constant, and n is the number of moles. Real gases, especially at high pressures, deviate from this behavior. Their responses can be modeled with the van der Waals equation: P-- nRT n² a + = 0 V-nb V2 Where a and b are material constants. For CO₂ a 3.5924 L'atm/mol², and b=0.04267 L/mol. Calculate P from both equations for CO₂ gas with 40 values of V between 0.01 and 1.5 and display the results in: 1- Three-column table where the values of Vand both P are displayed in the first, second, and third columns, respectively. 2-Plot V versus both P in two different plots in the same figure with a solid line, black color, with circle marker. Add a title, labels, and the grid to the plot. Make all texts bold with font size of 13. Take T-298K and n-3 moles.Let Ax = {a,b,...,z,—}, |Ax| = 27, denote alpahabet of letters in English text where - represents the space character between words. Let Px = {P₁, P2,..., P27} denote the probability of letters. 1) Estimate pi, by parsing the text "All Systems Red' by Martha Wells. To do this you have to parse the letters in the book and form a character vector x = = [1, 2,..., TN] where N is the number of letters in the book. (Turn all uppercase letters into lowercases and ignore the characters that are not in Ax). You may use Matlab or Python. Then you can estimate p; by its frequency in the text #(x₁ = ai) N where #(i = a;) denotes the number of times ï¿ = a¿ in x. Pi = (1)
- Vo l KB/S V:10 > موعد التسليم اليوم، 0 8:0 م Home work (Matrices) ۰ ۱۰ نقطة إضافة تعليق في الفئة 1. Find determinant of A in example 9 with two ways? 2. find A*B and B*A for the matrices A= 10 1 11 2 1- 2 3 B= %3D 3 0 0 4 2 1 0 1- 1- تم التسلیم عملك أضف تعليقك الخاصGiven bags are labelled to any or all the coins in every bag have an equivalent weight. Some bags have coins of weight ten g, others have coins of weight eleven gm. I choose some random coins severally from bags five to 1 Their total weight comes bent on 323 gm. Then the merchandise of the labels of the baggage having 11 gm coins is toiletI. Fermat's test consists of using Fermat's Theorem (an¹=1 (mod n)) with prime n. Just pick any number a E {1, ..., n-1} and check if it satisfies the expression. If not, then it must be a composite number, that is, it is not prime. II. Although Fermat's Theorem is used to check whether a number is prime or not, we can still obtain equality (an¹-1 (mod n)) even when n is not prime. E The numbers for which this situation occurs are called Carmichael numbers or pseudoprimes. III. Both the Miller-Rabin and AKS algorithms (checking a prime number) work for any type of input and are polynomial time. However, only AKS is deterministic. IV. The Miller-Rabin algorithm guarantees when a number is prime, but when it is composite (non-prime) it can only guarantee this characteristic in probabilistic terms. Only the following items are correct: A I, II, III B I, II, IV C I, III, IV D II, III, IV E I, II, III, IV
- Suppose that the equation ax b .mod n/ is solvable (that is, d j b, whered D gcd.a; n/) and that x0 is any solution to this equation. Then, this equation has exactly d distinct solutions, modulo n, given by xi D x0 C i.n=d / fori D 0; 1; : : : ; d 12. A discrede random varPable X has the followFny Probability distrbfution: the Value 2. 34 6 7 PO)C 2c 3C c2c4ad 20 d.6. AND Since there are two zeros on the board, let's determine the probability that you would be able to cover them on 2 consecutive turns. This means you'd have to roll a zero and then roll another zero. You can think of this as an AND probability. You need to roll 0 AND then you need to roll 0 again. Since the result of the first roll will have no influence on the result of the second roll, you can use the following rule: P(A and B) = P(A) * P(B) a) Determine P(0 and 0). b) Determine 1 - P(0 and 0). c) Write a sentence describing the meaning of 1 - P( Oand 0 ).