Engineering statistics Given that X-B (5, 0.7), find the following: (a) the probability of failure (b)...
7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1) (b) Find the expected value. (c) Find the variance.
Examination in probability theory and statistics Variant 9 1. Discrete distribution for X is given by the following table: Probability p ValueX Find distribution function fa) and median Me(0). Calculate mathematical expectation (the mean) M(x), 0.3 -10 0.4 10 0.2 20 0.1 40 variance (dispersion) Da, standard error ơ(X), asymmetry coefficient As(X) and excess Ex(X). 2. Calculate multiplier k. Find mode Mots, median Me(o), mathematical expectation (the mean) Mc) variance (dispersion) D(x) and standard error σ(x) for continuous distributions having...
Find the variance of random variable X. 7.. Let X be a continuous random variable whose probability density function is: -(2x3 + ar', if x E (0:1) if x (0;1) Find 1) the coefficient a; 2) P(O.5eX<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given X 8 -2 0 2 8
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
If n 5 and x 0.45, what is the probability of the following? (a) (b) (c) (d) X= 4 Xs3 X<2 X>1 (a) P(X- 4)= (Round to four decimal places as needed.)
Probability Theory and Statistics Exercise 11 1. Suppose that the p.dforisf(x)-F' ,x> , where σ is constant. Find the value of ELX) and Dr. 2. Suppose that the p.dfof (x.r is (x,y)- 1Sxy, 0SysI Find the value of D) 0 otherwise and D(). 3. Suppose that of x- - N(0.0.5), Y N(00.5) and .X.Y are independent. Determine the variance
Problem 4: (20 Points) X is a uniform random variable with parameters -5 and 5. Given the event B-VI > 3) 1. (5 points) What is the probability of the event B, P(B)? 2. (5 points) What is the conditional PDF, fxB()7 3. (5 points) Find the conditional expected value, E[X |B]. 4. (5 points) Find the conditional variance, var[X]B].
Homework in statistics ariant 14 1. Discrete distribution for X is given by the following table: Probabilities p Values X 0.2 40 0.1 0.5 4 0.1 50 0 20 10 20 Find distribution function fx) and median Me(x). Calculate expectation value (dispersion) D(X), standard error σ(X) , asymmetry coefficient As(X) and excess Ex(X) Mx), variance 2. Calculate multiplier k. Find distribution function fitz, mode Moty), median Meco, expectation M(x), variance (dispersion) D(x), standard error σ( for continuous distributions with the...
1. (10 points) Let X be a continuous random variable with the probability density function given by f(x)-4z if 0SaS1 and O otherwise (a) Find P(X sjIx> j) (b) Find the expectation and variance of X
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...