1.) What is the hypothetical likelihood that a considerably number

will be moved on a number 3D shape?

2.) What was the test likelihood of how often

a much number was really moved utilizing the table?

3.) If you roll a number solid shape a day and a half, how often would

you hope to roll the main?

4.) what number occasions did you really roll the main in the analysis?

5.) What is the hypothetical likelihood for rolling a number more prominent than 4?

6.) What was the exploratory likelihood of rolling a number more prominent than 4?

7.) What is the distinction among hypothetical and exploratory likelihood?

8.) If a vehicle production line checks 360 vehicles and 8 of them have deserts, the number of will have surrenders

out of 1260?

Number on Cube Frequency

1 8

2 3

3 9

4 6

5 4

6

9.) If a vehicle production line checks 320 vehicles and 12 of them have surrenders, the number of out of 560 will

NOT have deserts?

10.) You plant 30 African violet seeds and 9 of them sprout. Utilize trial likelihood to

foresee what number of will grow in the event that you plant 20 seeds?

Q3 Answer the following questions about bivariate normal random variables. a. Suppose X and Y are dependent bivariate normal random variables. Then the correlation between X and Y: is positive. equals zero. is negative. may be positive or negative, but is nonzero. cannot be determined without additional information. Submit Answer Tries 0/10 b. The bivariate normal distribution has location parameters /x and My. O True. False. Submit Answer Tries 0/10 c. Consider the countour plot of bivariate normal random variables (X, Y) when ux = 8. ox = 3. My = 6, cy = 5, and p = -0.7. The contours look like: concentric circles around the point (8. 6). concentric ellipses having center (8. 6) and tilted along a line that has positive slope. one straight line with slope -0.7. two straight lines, one with slope -0.7 and one with slope 0.7. concentric ellipses having center (8, 6) and tilted along a line that has negative slope. Submit Answer Tries 0/10Problem 8 [10 points = 2 + 8] Consider a bivariate random vector Z = (Z1, Z2) with independent components, each having the standard normal distribution. Introduce a bivariate vector Y = (Y1, Y2) with components defined as follows. Y1 = 271 -372 - 5 and Y2 = 3Z1 + 2Z2 + 4 1. Evaluate the mean vector, E [Y] = (E [Y], E[Y2]) 2. Derive the variance-covariance matrix for YSuppose (X, Y) follows bivariate normal distribution with parameters (M1, 01, /2, 02, p). (a) Define two new random variables Z1 and Z2 by Y - H2 X - /1 Z1 = X - /1 1 and Z2 = 1 - p2 P 01 02 Use the bivariate transformation technique to calculate the joint pdf of (Z1, Z2) and then prove Z1 and Z2 are independent standard normal random variables. (b) Now suppose #1 = 1, of = 2, /2 = 2, 02 = 1, and p = 0.5. Let U = (X + Y)/2 and V = (X - Y)/2. Compute the joint pdf of (U, V), and then argue that (U, V) follows a bivariate normal distribution. Identify the parameters. (c) In (b), identify the conditional distributions of U|V = 1 and V|U = 0.Problem 5. Suppose we have finite bivariate population {(21, 31), . .. ,(IN, yN)}. We assume N > 1. Let To and Ty be the population totals of the r- and y-measurements, respectively; let , and My be the population means of the x- and y-measurements, respectively; let o > 0 and o, > 0 denote the population variances of the x- and y-measurements, respectively. Let ory denote the population covariance. Just for reference, 1 Ory N (xi - MI) (yi - My) i=1 Suppose {(X1, Y1), . .., (Xn; Ym) ), where n > 1, denotes a random sample drawn WITH REPLACEMENT from this population. Let X and Y denote the sample means of the x- and y-measurements in the sample. What is true about the sample {(X1, Yl), . .. , (Xn; Ym)}? (a) (X1, Yi) is identically distributed to (X2, Y2), but they are not independent. (b) (X1, Yi) is independent of (X2, Y2), but the distributions of these two bivariate random variables will be different. (c) Since the pairs (Xi, Y;) are drawn uniformly at random from the population and since the sample is selected with replacement, the pairs (X1, Yi) and (X2, Y2) are independent and identically distributed bivariate random variables. (d) Since Y1 is not necessarily independent of X1, the bivariate random variable (X1, Y1 ) cannot be independent of the bivariate random variable (X2, Y2). (e) Both (a) and (d) are correct. (f) None of the above