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In Problems 1–6, find the mean, variance, and standard deviation.
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- .If the variance of a Poison variate is 3. Find the probability that, ne. (1) X = 0 (ii) 1sx<4 eor (iii) 0arrow_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_forward8- Find the mean and variance of X? X 1 2 3 4 f(x) 1/9 2/9 3/9 2/9 1/9 a) 3, 2/3 1903 b) 2, 4/3 c) 3, 4/3 d) 2, 2/3arrow_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_forwardExample 9-4. X is a normal variate with mean 30 and S.D. 5. Find the probabilities (i) 26 45, and (iii) |X – 30l > 5.arrow_forwardEX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.arrow_forwardShow that E [ X – m]3 = E(X)3 - 3m, o? - m? where m, and o are the mean and variance of X respectively.arrow_forwardProb. 3 Let X be a random variable with cumulative distribution function (cdf) given by (1-e-x², x ≥ 0 ={1,- x<0 Find the probability that the random variable X falls within one standard deviation of its mean. Fx (x) =arrow_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_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 io patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: E(X)=0.4 and V(X)=0.384 O None of these O E(X)=0.5 and V(X)=0.475 O E(X)=0.3 and V(X)=0.291arrow_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_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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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