Concept explainers
In Problems 1–6, find the mean, variance, and standard deviation.
2.
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
- Q. 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 Show that E { X – m3 = E(X)³- 3m of-m, where m and of are the mean and variance of X respectively. %3Darrow_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_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_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_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_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_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_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_forwardExample 9-32. Show that the mean value of positive square root of a y (u) variate is T(u +; )/T(µ). Hence prove that the mean deviation of a normal variate from its mean is V2/T , where o is the standard deviation of the distribution.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education