Let X1, X2, X3, X4, X5, and X6 denote the numbers of blue, brown, green, orange,...

Let X1, X2, X3, X4, X5, and X6 denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these Xi's have a multinomial distribution. Suppose it is claimed that the color proportions are p1 = 0.22, p2 = 0.13, p3 = 0.18, p4 = 0.2, p5 = 0.13, and p6 = 0.14. (a) If n = 12, what is the probability that there are exactly two M&Ms of each color? (Round your answer to four decimal places.) Correct: Your answer is correct. (b) For n = 20, what is the probability that there at most eight orange candies? [Hint: Think of an orange candy as a success and any other color as a failure.] (Round your answer to three decimal places.) (c) In a sample of 20 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 8? (Round your answer to three decimal places.)

Expert Solution

milcah answered 1 year ago

Case Y X1 X2 X3 X4 X5 X6 1 43 45 92 61 39 30 51...

Case Y X1 X2 X3 X4 X5 X6 1 43 45 92 61 39 30 51 2 63 47 73 63 54 51 64 3 71 48 88 76 69 68 70 4 61 35 86 54 47 45 63 5 81 47 85 71 66 56 78 6 43 34 51 54 44 49 55 7 58 35 70 66 56 42 67 8 71 41 64 70 57 50 75 9 72 31 81 71 69 72 82...

Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove...

Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove that U is a subspace of F4. (b) Find a basis for U and prove that dimU = 2. (c) Complete the basis for U in (b) to a basis of F4. (d) Find an explicit isomorphism T : U →F2. (e) Let T as in part (d). Find a linear map S: F4 →F2 such that S(u) = T(u) for all u ∈...

Using Y as the dependent variable and X1, X2, X3, X4 and X5 as the explanatory...

Using Y as the dependent variable and X1, X2, X3, X4 and X5 as the explanatory variables, formulate an econometric model for data that is (i) time series data (ii) cross-sectional data and (iii) panel data – (Hint: please specify the specific model here not its general form).

Let X1, X2, X3, X4, X5 be independent continuous random variables having a common cdf F...

Let X1, X2, X3, X4, X5 be independent continuous random variables having a common cdf F and pdf f, and set p=P(X1 <X2 <X3 < X4 < X5). (i) Show that p does not depend on F. Hint: Write I as a five-dimensional integral and make the change of variables ui = F(xi), i = 1,··· ,5. (ii) Evaluate p. (iii) Give an intuitive explanation for your answer to (ii).

The values of X1, X2, X3, X4 and X5 are .1, .2, .08, .2 and .3....

The values of X1, X2, X3, X4 and X5 are .1, .2, .08, .2 and .3. Explicate the meaning of those numbers for the Z score. What are the prospects of this firm? Discuss thoroughly.

Let X1, X2, X3, and X4 be a random sample of observations from a population with...

Let X1, X2, X3, and X4 be a random sample of observations from a population with mean ? and variance ?2. Consider the following two point estimators of ?: b1= 0.30 X1 + 0.30 X2 + 0.30 X3 + 0.30 X4 and b2= 0.20 X1 + 0.40 X2 + 0.40 X3 + 0.20 X4 . Which of the following constraints is true? A. Var(b1)/Var(b2)=0.76 B. Var(b1)Var(b2) C. Var(b1)=Var(b2) D. Var(b1)>Var(b2)

The prices of inputs (x1,x2,x3,x4) are (4,1,3,2): (a) If the production function is given by f(x3,x4)...

The prices of inputs (x1,x2,x3,x4) are (4,1,3,2): (a) If the production function is given by f(x3,x4) =min⁡{x1+x2,x3+x4} what is the minimum cost of producing one unit of output? (b) If the production function is given by f(x3,x4)=x1+x2 +min⁡{x3+x4} what is the minimum cost of producing one unit of output?

Let x1, x2,x3,and x4 be a random sample from population with normal distribution with mean ?...

Let x1, x2,x3,and x4 be a random sample from population with normal distribution with mean ? and variance ?2 . Find the efficiency of T = 17 (X1+3X2+2X3 +X4) relative to x= x/4 , Which is relatively more efficient? Why?

4. Determine the number of integer solutions of x1 + x2 + x3 + x4 =...

4. Determine the number of integer solutions of x1 + x2 + x3 + x4 = 17, where a. xi ≥ 0, 1 ≤ i ≤ 4 b. x1, x2 ≥ 3 and x3, x4 ≥ 1 c. xi ≥ -2, 1 ≤ i ≤ 4 d. x1 , x2 , x3 > 0 and 0 < x4 ≤ 10

Let X1, X2, X3 be independent having N(0,1). Let Y1=(X1-X2)/√2, Y2=(X1+X2-2*X3)/√6, Y3=(X1+X2+X3)/√3. Find the joint pdf...

Let X1, X2, X3 be independent having N(0,1). Let Y1=(X1-X2)/√2, Y2=(X1+X2-2*X3)/√6, Y3=(X1+X2+X3)/√3. Find the joint pdf of Y1, Y2, Y3, and the marginal pdfs.

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