Mathematics, 24.03.2020 01:24 Wolfgirl2032
The random variable X measures the concentration of ethanol in a chemical solution, and the random variable Y measures the acidity of the solution. They have a joint probability density function f (x, y) = A (20 - x - 2y), 0 lessthanorequalto x lessthanorequalto 5, 0 lessthanorequalto y lessthanorequalto 5 and f (x, y) = 0 elsewhere. (a) What is the value of A? (b) What is P (1 lessthanorequalto X lessthanorequalto 2, 2 lessthanorequalto Y lessthanorequalto 3)? (c) Construct the marginal probability density functions for X and Y. (d) Are the ethanol concentration and the acidity independent? (e) What are the expectation and the variance of the ethanol concentration? (f) What the expectation and the variance of the acidity? (g) If the ethanol concentration is 3, what is the conditional probability density function of the acidity? (h) What is the covariance between the ethanol concentration and the acidity? (i) What is the correlation between the ethanol concentration and the acidity?
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Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?
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The random variable X measures the concentration of ethanol in a chemical solution, and the random v...
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