Consider the following exponential probability density function. f(æ) = 2 for x >0 a. Which of the following is the formula for P(x < xo) ? Го 1 P(x < xo) 2 2 P(x < xo) =1 3 Р(т < tо) %3D 1-е 2о Formula #2 b.Find P(x < 1) (to 4 decimals). 0.3935 c. Find P(x > 4) (to 4 decimals). 0.3679 d.Find P(x < 6) (to 4 decimals). e. Find P(1 < x < 6) (to 4 decimals).

The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 32x²e-4x The kinetic energy of the particle is Y = 1/mX². Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.) x >0.

Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 14 1 38 2 38   x P(X=x) 0 18 1 18 2 34   x P(X=x) 0 −310 1 110 2 15 3 1   x P(X=x) 0 0.74 1 0.0 2 0.54   x P(X=x) 0 110 1 15 2 35   x P(X=x) 0 0.18 1 0.76 2 0.0

Q.2 h(x)==-exp 8 You are given h(x) with the random variable X taking only positive values, -7)+ X 1 X 1 -exp +-expl 2 X 8 24 a. Check if h(x) is a valid pdf (probability density function)? b. Obtain the CDF of X. c. Obtain the mean of X. 4 -exp 80 X 10 ,x≥0

The probability of the closing of the ith relay in the circuits shown is given by pi. Let P₁= 0.6, P2=0.1, pa=0.5, pa=0.7, Ps= 0.3. If all relays function independently, what is the probability P that a current flows between A and B for the respective circuits? (b) (a) P= 0.1167 (b) P 0.5156 e B

Harrison is a sports statistician and is interested in the number of strikeouts by a starting pitcher over the past five years for a certain professional baseball league. He randomly selects 471 games and records the number of strikeouts by one of the starting pitchers in the game, where the pitcher for the home or visiting team is selected at random. Harrison records the total number of strikeouts by the starting pitcher in that game, x, and the probability of each value, P(x), as shown in the table provided. Find the mean and the standard deviation of the probability distribution using a TI-83, TI-83 Plus, or TI-84 graphing calculator. Round the mean and standard deviation to three decimal places. Number of strikeouts x   P(x)0                                              0.0161                                              0.0452                                              0.0593                                              0.0834                                              0.0985…

Consider the probability density function 1 if x -4 + (x+4) Find the median. Select one: -3 О -5 O 1 O 0.5

Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day io patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: E(X)=0.4 and V(X)=0.384 O None of these O E(X)=0.5 and V(X)=0.475 O E(X)=0.3 and V(X)=0.291

The probability that a regularly scheduled flight departs on time is P(D) = 0.83; the probability that it arrives on time is P(A) = 0.82; and the probability that it departs and arrives on time is P(D NA) = 0.78. Find the probability that a plane departed on time, given that it has .arrived on time

he following table shows the returns of two types of investments, stocks (x) and bonds (y), under two different scenarios: boom and recession. The frequency f(∙) indicated the probability of boom and recession, and it is the same for any type of investment. Suppose you diversify your investments by splitting your funds half and half between stocks and bonds. That is, z = 1⁄2x + 1⁄2y. Find E(z) and the riskiness (standard deviation) of z.