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Let X be a random variable that is equal to 0 with probability 0.4 and to...
1. Here is the probability distribution for a random variable x: Value of X Probability 0.4 0.6 a. (4 pts) Find the mean and the standard deviation of this distribution. Show all work. b. (4 pts) Let Y 3X -2. Find the mean and the standard deviation of the distribution of Y Show all work and any rules you use c.(4 pts) Now let 2 3x2-2, Find the distribution of Z by completing the table below Value of Z Probability...
3. Let X be random variable with probability density function x(x)4 for 0 x 1, (Note: fx (x) = 0 outside this domain.) (a) Find E[X] and Var[X] (b) Let Y- X2 +5. Find E[Y] and Var[Y]. (c) Find PX 112 ).
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
3. Let X be an exponential random variable with parameter 1 = $ > 0, (s is a constant) and let y be an exponential random variable with parameter 1 = X. (a) Give the conditional probability density function of Y given X = x. (b) Determine ElYX]. (c) Find the probability density function of Y.
Let X be a continuous random variable with probability density function fX(x)=2x for 0 < x <1. What is the expected value of X.
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval 0<x<2 (a) What is the support of X? (b) Letting S be the support of X, pick two numbers a, b e S and compute Pa<x<b). Draw a graph that shows an area under the curve y = f() that is equal to this probability. (c) What is Fx (2)? Draw a good graph of y=Fx (I). (d) What is EX? (e) What is...
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.85 and 0.96? (c) What is the probability of generating a number greater than 0.88? (a) Choose the correct graph of the uniform density function below. ОА. OB. OC. A Density Density A Density ON ON...
In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (0) below 0 0.278 10.573 3 0.027 4 0.004 5 0.001 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because theof the probabilities is (Type whole numbers. Use ascending order) (b) Draw a graph of the probability distribution Describe the shape of...