Please show the steps in detail. 1. Let ZNb (2, (a) Calculate P(Z > 8)
6. Let α be such that Icel < 1 . Let φ,(z) = ,,. Show that φα(z) maps B(0, 1) zEC: lzl 1) one-to-one onto B(0, 1) and that the inverse map φα(z)-1 is φ,(z). 2
4. Let Z ~ N(0,1) be a standard normal variable. Calculate the probability (a) P(1 <Z < 2). (b) P(-0.25 < < < 0.8). (c) P(Z = 0). (d) P(Z > -1).
Vx+1-1 Evaluate: lim x>0 х Please solve it in detail and show all your steps./
PLEASE HELP WITH PROOF!! 8. Let an > 0 for all n in 1. Show that if an converges, then Ĉ vanın converges. [Hint: Expand [van - (1/n)]2.) N =
Exercise 3.38. Let the random variable Z have probability density function 24 fz(z) = -1 <z<1 otherwise. (a) Calculate E[Z]. (b) Calculate P(0 <Z<į). (c) Calculate P(Z < į 12 > 0). (d) Calculate all the moments E[Z"] for n= 1,2,3,... Your answer will be a formula that contains n.
(1) Let qn(x)-IT-1 (z-zi) where the xi, į = 1, , n are equally spaced: zi+1-z-h for some h > 0. Let a (a) Show 21 and b zn. zela阎 (b) Show
QUESTION 26 AND 31 PLEASE SHOW STEPS THANK YOU SO MUCH J-2 J-V4-z² Ji 26. Let be the region below the paraboloid x2 + y? = z – 2 %3D that lies above the part of the plane * + Y + z = I in the first octant. Express f (x, y, z) dV as an iterated integral (for an arbitrary function J). 27. Assume J (ª, Y, 2) can be expressed as a product, f (x, y, z)...
please show you steps, and add some exppanation if possible. Thank you! 5. Let X associated probabilities P(X = x)-/(2) be a discrete random variable. The following table shows its possible values r and the () 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X s 1), and P(X0.5 or Xx> 2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X
Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places. Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places. p(Z > 0.53)- Plz <-0.67) P (0.48 < Z < 1.94)- 0
Please show your steps in details. Z is a complex number. 3. Let /(z= |Re z||Im zſ for all ze C. Show that $(z) is not differentiable at z=0.