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- Suppose W1 = span(v1, v2, v3, v4), W2 = span(v1, v2, v3, v5), W3 = span(v1, v2, v3, v4, v5) and dim(W1) = dim(W2) = dim(W3) = 4. Show that W1 = W2.Suppose that factor AB is significant and that both A and B are significant. This is called Inverse relation Strong heredity Weak heredity None of theseVariety reduction is generally known as:(A) Less varieties(B) Simplification(C) Reduced varieties(D) None of the above
- A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.03 0.02 1 0.07 0.20 0.08 2 0.05 0.14 0.31 (a) Given that X = 1, determine the conditional pmf of Y—i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.) y 0 1 2 pY|X(y|1) (b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.) y 0 1 2 pY|X(y|2) (d) Given that two hoses are in use at the…A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.05 0.01 1 0.07 0.20 0.08 2 0.05 0.14 0.30 (d) Compute the marginal pmf of X. x 0 1 2 pX(x) Compute the marginal pmf of Y. y 0 1 2 pY(y) Using pX(x), what is P(X ≤ 1)? P(X ≤ 1) =Direct product AxB is isomorphic CxD.
- (b) Write V as a set of ordered pairs. (Enter your answer in roster notation.) (c) Write the domain set of V. (Enter your answer in roster notation.) Write the co-domain set of V. (Enter your answer in roster notation.)3. Give the domai of y= 6-X using set builder notation. 4. A person is earning P600 per day to do a certain job. Express the total salary S as a function of the number n of days that the person works. 5. A taxi ride costs P40.00 for the first 500 meters, and each additional 300 meters (or a fraction thereof) adds P3.50 to the fare. Use a piecewise function to represent the taxi fare in terms of the distance d in meters 6. A certain chocolate bar costs P35.00 per piece. However, if you buy more than 10 pieces, they will be marked down to a price of P32.00 per piece. Use a piecewise function to represent the cost in terms of the number of chocolate bars bought.show that if Λ ∈ Rn and if it meets: • ≿ a weak order as to Λ • (strict dominance) if a_i > b_i ∀i ∈ {1,2,3,...,n} ⇒ a ≻ b • (continuity) a ≻ b, b ≻ c ⇒∃λ ∈[0,1]. ∋.(λa+(1−λ)c)∼b ⇒∃f ordinal value function representing the preferences of the decision maker.