12 Points A dealer's profit, in units of $10000, on a new truck is given by the function Y = X2, where X is a random variable having following density function: 0.49 ƒ(x) = { ² using the density function of Y find the probability the the profit on the next new truck sold by this dealership will be less than $2000. 0.09 ☐0.29 0.69 2(1-x), 0
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- Given the probability density function f(x)=16f(x)=16 over the interval [4,10][4,10], find the expected value, the mean, the variance and the standard deviation.Expected value: Mean: Variance: Standard Deviation:1 Given the probability density function f(x) = 4 over the interval [1, 5], find the expected value, the mean, the variance and the standard deviation. Expected value: Мean: Variance: Standard Deviation:b) Consider a random variable X which takes on values 1 and 2 with probability 0.25 and 0.75, respectively (i.e. P[x = 1] = 0.25 and P[x = 2] = 0.75 i) Determine the mean and variance of X. ii) Plot the probability density function (pdf) and probability distribution function (PDF) of X
- The yearly cost in millions of dollars caused by Godzilla rampaging in Tokyo is a random variable with an exponential probability density functionf(x) = 0.45e−0.45x, [0, ∞) Find the median yearly cost (in millions of dollars) of Godzilla’s rampages.QI Since h(t) = 1+t 1>0 i. The survival function is given by? ii. Probability density function is given by iii. The mean time to failure(MTTF) of the component is given by(Continuous random variable) In a city, the daily electricity consumption (millions of kWh) is a random variable whose probability density is: f(x) - ਵਿਆ = 0 x xe 3 six>0 six<0 The city's electric power plant has a daily capacity of 12 million kWh. a. Verify that the given function is a probability density function. b. Calculate the probability that the power plant cannot meet the demand for electric power.
- 3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.Y is a continuous random variable with the probability density function pictured. what is the mean of y?4.32 Weekly CPU time used by an accounting firm has probability density function (measured in hours) given by | (3/64)y²(4 – y), 0The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8If probability density function of a random varíable X is f(x) = x² for –1SXS1, and %3D O for any other value of x %3D is then, the percentage probabilityPThe proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2x + 4 0 < x<1 f(x) = - 0, 5 elswhere Find the stàndard deviation of above stated continuous random variable (X)SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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