2. Show that a. P.(-x) =(-1)*P(x) b. Px.(0) - (-1) 2(!) c. P(0) - 0 3. Prove that j «P.com j«P«6?P.:(}é 4. Evaluate j <P:6)Ps(x)dt 5. Use Rodrigue's formula to calculate P (4)
6. Assume that X and Y are independent and follow normal distributions with px (a) evaluate P(X + Y 〉 24) (2pt) (b) find x such that P(x 〈 X-Y 〈 10) 20, σ = 4 and μγ-10, σ = 2. 0.2 (3pt)
2. Prove that for any fixed real numbers p and g, the equation 2xr + px+q + log2(x2 + px + q) + x2 + px = 2019 has at most two real number solutions.
2. Prove that for any fixed real numbers p and g, the equation 2xr + px+q + log2(x2 + px + q) + x2 + px = 2019 has at most two real number solutions.
Evaluate, 23:58 2 x 2 + y dxdy by converting to polar coordinates.
2) Consider a random variable with the following probability distribution: P(X-0)-0., Px-1)-0.2, PX-2)-0.3, PX-3) -0.3, and PX-4)-0.1 A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated values. How do these summary measures compare to the...
Consider the linear system x′=Px where P is a 2×2 constant
matrix. assume P has only one eigenpair
Consider the linear system x' = Px where P is a 2 x 2 constant matrix. Assume P has only one eigenpair Then the general solution of this system might have the form: (-20) 2 Ite (a) C 21 le-24 C[***]+O (b) c(-7*]+c=[e (6) c [**] +c[-e* (a) C[*]+c [64 le 21 (1+)e 24
u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4 initial prices px,py and final prices p′x,p′y. For THE problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change = optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect
9) What are the components (px, py and p.) of vector p if p = nxm p= nxm m= (1 m)x+(2 m) + (-3 m). m = (-3 m)+(-2 m)ỹ + (4 m)?
AS AS W P- X Price Level Price Level Price Level AS, AS, PX PX P AD AD, AD, O Q, Q, 0 Q,, 0 0 0 Real GDP Real GDP Real GDP (A) (C) ADAD, Refer to the diagrams, in which AD, and AS, are the "before" curves and AD and AS2 are the "after" curves. Other things equal, an increase in investment spending is depicted by Multiple Choice o o o O B and C
Given: Р P5 Some) Px P3 P 1:0 B -Dd Pit MR Q and assuming that all lines in the diagram are straight lines and that the following approximate measurements were made: O to P1 $10 o to Q1 20 million P1 to P2 $15 Q1 to Q2 10 million P2 to P3 $7 Q2 to Q3 10 million P3 to P4 $8 P4 to P5 $20 Please refer to the image and measurements above: i. A is called: ;...