3. Severe snowstorm is defined as a storm with snowfall exceeding 10 inches. Let X be the amount of snowfall in a sever...
Will rate! Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the CDF, cumulative density function, is the following F(x) - Use the cumulative density function to obtain the following. (If necessary, round your answer to four decimal places) (a) Calculate P(X s 1). (b) Calculate P(0.5 s X s 1). (c) Calculate P(x > 1.5). (d) what is the median checkout duration μ? [.olve o.s-r(p)]. (e) Obtain the probability density...
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the CDF, cumulative density function, is the following:\(F(x)= \begin{cases}0 & x<0 \\ \frac{x^{2}}{4} & 0 \leq x \leq 2 \\ 1 & 2 \leq x\end{cases}\)Use the cumulative density function to obtain the following. (If necessary, round your answer to four decimal places.)(a) Calculate P(X ≤ 1).(b) Calculate P(0.5 ≤ x ≤ 1).(c) Calculate P(x>1.5).(d) What is the median checkout duration \tilde{μ} ?...
Distributions Consider the function f(x)3+1-2-4 0334 (a) Can this function be used as a probability density function? If not, normalize it such that it can, and let that be p(x) (b) Create a CDF of your probability density function, p(x) (c) Compute the expected value and variance of p(z) (d) What is the 90th percentile value of p() Distributions Consider the function f(x)3+1-2-4 0334 (a) Can this function be used as a probability density function? If not, normalize it such...
Problem 3. (12 points) Let X denotes the amount of time a book on two-hour reserve is actually checked out, and suppose the CDF is 2/4 0, if xs0 1, if x 22 (1) Find P(0.5 s X s 1). (2) Find P(x>1.5). (3) What is the mean (i.e., expected value for) checkout duration μ? (4) What is the median checkout duration (5) Obtain the PDF for X.
Assess a subjective triangular probability distribution for the random variable, X, where X is defined as the amount of snowfall you think we will get in our next snowstorm in inches. Suppose that you expect your commute to increase in minutes according to the function . What is the expected increase in your commute for the next snowstorm? Estimate E[f(X)] by creating simple Monte Carlo simulation in Excel. Here are some equations for the triangular distribution that may help you:...
c 3. Let X have density fx () = 1+1 -1<<1. (a) Compute P(-2 < X <1/2). (b) Find the cumulative distribution Fy(y) and probability density function fy(y) of Y = X? (c) Find probability density function fz() of Z = X1/3 (a) Find the mean and variance of X. (e) Calculate the expected value of Z by (i) evaluating S (x)/x(x)dr for an appropriate function (). (ii) evaluating fz(z)dz, pansion of 1/3 (ii) approximation using an appropriate formula based...
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 0x<0 F(x) = x OSX<4 1 45x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X S 2). (b) Calculate P(1.5 SXS 2). (c) Calculate P(x > 2.5). (d) What is the median checkout duration ? (solve 0.5 = F)]. (e) Obtain the density function f(x). f(x)...
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. \(F(x)= \begin{cases}0 & x<0 \\ \frac{x^{2}}{25} & 0 \leq x<5 \\ 1 & 5 \leq x\end{cases}\)Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)(a) Calculate P(X ≤ 2)(b) Calculate P(1.5 ≤ x ≤ 2).(c) Calculate P(X>2.5).(d) What is the median checkout duration \tilde{μ} ? [solve 0.5=F(\tilde{μ})].(e) Obtain the density function f(x).f(x)=F'(x)=(f)...
[6] 3. Let z be the amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train. Suppose that the density curve is as pictured Density 0.05 20 Minutes (a) What is the probability that is less than 5 minutes? (b) What is the probability that is between 10 and 12 minutes? 4/9 (c) Find the value c for which P(x <c) -0.9.
Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value: a) between 29 and 36 b) between 22 and 35 Let x be a continuous random variable that is normally distributed with a mean of 80 and a standard deviation of 12. Find the probability that x assumes a value a) greater than 69 b) less than 73 c) greater...