Concept explainers
YOUR TURN 1 Repeat Example 1 for the probability density function
EXAMPLE 1 Expected Value and Variance
Find the expected value and variance of the random variable
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Calculus For The Life Sciences
- Combined probability density function of continuous random variables X and Y -∞<x<∞ , -∞<y<∞ If it is assumed to be defined in the range, which of the following is / are true?arrow_forwardA filling station recieves its supply of gasoline once a week. Its weekly volume of sales in thousands of gallons is a random variable with probability density function f(x) = 5*(1-x)4 for 0 less than or equal to x and x less than or equal to 1 and f(x) = 0 otherwise. Find the capacity of its tank so that the probability of its supply being exhausted in a given week is 10%arrow_forwardA continuous random variable X has the probability density function f(x) = (4-x)/8, 0 ≤ x ≤ 4. Find the expected value of Xarrow_forward
- The random variable X models the loss in thousands of dollars due to a fire in a commercial building. Its density function is f(x) = 0.005*(20-x) for 0 being less than or equal to x and x being less than or equal to 20 and f(x)= 0 otherwise. Given that a loss due to the fire exceeds $8000, find the probability the loss exceeds $16000.arrow_forwardA random variable X has the probability density function as f(x) = Ax(9-X2) 0 ≤ x ≤ 3 = 0 otherwise Find the value of A, the mean and the standard deviation of X.arrow_forwardBattery life between charges for the Motorolla Droid Razr Maxx is 20 hours when the primary use is talk time. The battery life drops to 7 hours when the phone is primarily used for Internel applications over cellular. Assume that the battery life in both cases follows an exponential distribution. a. Show the probability density function for battery life for the Droid Razr Maxx phone when its primary use is talk time. b. What is the probability that the battery charge for a randomly selected Droid Razr maxx phone will last no more than 15 hours when its primary use is talk time? c. What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last more than 20 hours when its primary use is talk time? d. What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last no more than 5 hours when its primary use is Internet Applications?arrow_forward
- a. Explain the difference between the method of moment generating function and the method of incarnation to find the probability density function of a random variable b. Let X1, X2, X3 ,,,,, each of them has Poisson distribution with parameter lamda 1, lamda2, lamda3,........ i. Get the probability distribution of Y=X1+X2+....Xn ii. Get the mean and variance of Y c. Y1 and Y2 be a joint probability function as shown below in the screenshot imageU=Y1/(Y1+Y2), Using the method of incarnation (Jacobian), find the probability density function of Uarrow_forwardThe random variable X has a uniform density function over the interval [-1, 1]. a. Sketch the probability density function of X. Find the mean and variance of X .arrow_forwardSizes of insurance claims can be modeled by continuous random variable X with probability density f(x) = c(10 - x) for 0 < x < 10 and f(x) = 0 otherwise, where c is some constant. What is the value of c? What is the probability that the size of a particular claim is no more than 5 and what is the probability that the size is more than 2?arrow_forward
- I. The length of time required by students to complete a 1-hour exam is a random variable X (in hours) with probability density function f(x) = 45(x3 + 1) for 0 < x < 1 and f(x) = 0 for x • • • • • • otherwise. Randomly select a student from this class. Whatistheprobabilitythatthecompletiontimeforthisstudentisatleast50minutes? Note that 40 minutes is equal to 40/60 hr. What is the probability that completion time is between 20 and 40 minutes? Determine the mean and variance of completion time. What is the CDF Graph the CDF Graph the PDF II . The average American eats 2,000 calories per day with a standard deviation of 500 calories. If this distribution follows a normal distribution, (a) What is the probability that someone eats between 2,000 and 3,000 calories per day? (b) How many calories corresponds to the 70th percentile? III. Draw a picture (Venn Diagram) for the following distributions. Additionally, find the fol- lowing probabilitis if P(A) = 0.4 and P(B) = 0.3 and P(A ∩…arrow_forwardAn electronic device contains two circuits. The second circuit is a backup for the first and is switched on only when the first circuit has failed. The electronic device goes down when the second circuit fails. The continuous random variables X and Y denote the lifetimes of the first circuit and the second circuit and have the joint density function f(x, y) = 24/(x + y)4 for x, y > 1 and f(x, y) = 0 otherwise. What is the expected value of the time until the electronic device goes down? What is the probability density function of this time?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage