y P(y) 0 0.64 1 0.25 4 0.11 E(y²) .¹ E(2√Y)
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- Determine, a) First two moments about the origin. b) The second moment about the mean.Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).Suppose Y - Uniform(01, 02) where the parameters and 02 take the values 1 and 5 respectively. Compute the probability P(Y < y) when y=4.71.
- 3. Which exponential probability density has mean u = ?Prob.5 Find the mean, the median, and the mode of the random variable X with the following probability density functions: (a) Gaussian distribution with parameters μ and o². (b) Exponential distribution with parameter 1. (c) Beta distribution with a = 3 and b = 4. (d) Uniform distribution in the interval (a, b).Q4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.
- Let X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0.Fourth letter of my surname is "İ".The table gives the joint probability distribution of the number of sports an individual plays (X) and the number of times she may get injured while playing (Y) X=1 X=2 X=3 0.12 0.08 0.15 0.06 0.05 0.05 0.10 0.03 0.15 0.15 0.04 0.02 Y=4 Y=3 Y=2 Y=1 The covariance between X and Y, oxy, is (Round your answer to two decimal places Enter a minus sign if your answer is negative) The correlation between X and Y, corr(X, Y), is (Round your answer to two decimal places Enter a minus sign if your answer is negative.) An increase in the number of sports an individual plays will tend to * the number of times she may got injured while playing
- If the joint probability distribution of X and Yis given by: (picture)Find P(X ≤ 2, Y = 1)Find P(X + Y = 4)Find P(X>Y )Find P(X > 2, Y ≤ 1)b. The table below shows the joint probability mass function for the discrete random variables X and Y. Y = 1 Y = 2 X = 0 X = 1 X = 2 0.07 0.23 0.18 0.05 0.29 0.18 Calculate and interpret the covariance between variables X and Y i.e. Cov(X,Y).