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In Problems 1–6, find the mean, variance, and standard deviation.
3.
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- Suppose that f (x) = x / 8 for 3 < x < 5. Determine the mean and variance of x.arrow_forward8 Show that E { X – m3 = E(X)³- 3m of-m, where m and of are the mean and variance of X respectively. %3Darrow_forwardQ. 4 The pdf of the age-of babies, x years, being brought to a clinic is given by /(x) =D 제(2-x); 0arrow_forwardCheck whether the mean and the variance of the following distributions exist: a a. fx (x) = -00 < x< 0 (a is positive constant) T(a²+x²) b. fx(x) = {2* {2x3 x21 elsearrow_forward1. In an epidemic, the probability of having S|D is 0.2 and P(D) = 0.1. P(S|D') = 0.04 and P (D') = 0.01. What is the P(D|S)? 2. The relationship between weight and age was found to have a linear relationship, with expression weight= 3.0 (age) +10. Predict the weight of a girl whose age is 20 years? 3. A. If a z score of 1.95 is equal to a p of 0.9744, what proportion is greater than1.95 B. From question A, what proportion is between the mean and 1.95? 4. If a the constant for a regression is 0.8 and the standard deviation for the x variables is 4 while the standard deviation for the y variables is 6. What is the correlation coefficient r? 5. In a class of 20 students, twelve take mathematics and genetics, while eight take genetics only. What is the probability of selecting a student who takes only mathematics?arrow_forwardSuppose 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 10 patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: None of these E(X)=0.5 and V(X)=0.475 E(X)=0.4 and V(X)=0.384 E(X)=0.3 and V(X)=0.291arrow_forward6. An optical device is used to detect the passage of cars in a single lane of a downtown street. Because there must be at least half a second between successive cars, it is assumed that the times T; between = 0.50 + Si, where S1, S2, ··. are independent exponential (A) random cars are of the form T; variables. (a) Find the mean and variance of each T;. (b) Let Y, be the time at which the nth car passes the detector. Calculate the mean and variance of Yn. (c) Under what conditions is Yn approximately normally distributed and why? (d) When n = 50 and A = 0.10, calculate the approximate probability that Yn exceeds 500 seconds.arrow_forward19. In Saint Tropez, the probability that it rains on a given day is 10%. Given that it rains, the amount of rain has a density of f(x) = (1/3)e-/3. Find the variance of the amount of rain on a given day. A. 0.9 B. 1.7 C. 3.0 E. 9.0 D. 4.4arrow_forwardCheck whether the mean and the variance of the following distributions exist: a. fx(x) = -00 < x < ∞ (a is positive constant) T(a²+x²) b. fx(x) = {2x3 x 2 1 else %3Darrow_forward4. In the study of human metabolism, it is known that daily calorie intake of a person age 25 above primarily affects the variability in weight gain. Scientists conducted an experiment to come up with a working formula of how much will be the average weight y (in kgs.) of a person age 25 if the person regularly has x calories of daily net calorie intake. It was shown that, on the average, y is related to x by the following relationship Y = In [x+ sin² (7)] + 50, x > 1. It was also observed that the each year the average weight of a person age 25 changes at a rate 1.5 kgs. per year. How fast is the average daily net calorie intake of a person changing when the person has 4 calories of daily net calorie intake?arrow_forwardFor any variable X, if: the standard deviation = and the variance = Var(X) Which of the following statement is true: Select one: a. SD < Var(X) O b. (SD)² = Var(X) (SD) C. SD = [var(x)]²arrow_forward2.3-1. Find the mean, variance, and index of skewness for the following discrete distributions: (a) f(x) = 1, x = 5. (b) f(x) = 1/5, (c) f(x) = 1/5, (d) f(x) = x/6, (e) f(x)= (1+x))/5, (f) f(x) = (2-x))/4, x= 1, 2, 3, 4, 5. x = 3, 5, 7, 9, 11. x = 1, 2, 3. x = -1,0, 1. x = -1, Q. 1.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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