The density function of a continuous random variable X is shown below. Find (a) the mode. (b) the median, and (c) the mean. -x(1-x²) -0.4 ≤x≤1 f(x) = (2500 441 otherwise
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- Let X - N (u, 1) and S? - x? (k) where X and S? are independently distributed. Find: VEX and its parameters. S (a) the distribution of () (b) Е SThe standard normal probability function is used to describe many different populations. Its graph is the well-known normal curve. This function is defined below. Give the intervals where the functions is increasing and decreasing. f(x) = 1 -x²14 √3xNeed help with this, please be clear and explain this. Will vote.
- The lifetime of a machine part has a continuous distribution: Osxs 40 fx(x) = { (10+ x)? else a. Calculate the probability that the lifetime of the machine part is more than 4. b. Calculate the expectation of life of this machine c. Calculate the variance d. Calculate the probability that the lifetime of the machine part is more than 4 given that is lasts for less than 12Please do a and b and please show stepsQ#4. Let X have a binomial distribution with 07 and p = Determine P(X = 1), P(X=;), P(X = 3), P(X = 6) and P(X < 2). %3D Note: Where R is the last digit of your registration number Solution#4 (to be typed here by the student)
- If the number of random sleigh sightings x follows a Poisson distribution with a mean = 1.7, then find the probability of x sightings. Find P(x = 4).(Round to four decimal places.)P(x = 4) =The lifetime of a certain lightbulb is a random variable with the expectation of 9000 hours and a standard deviation of 400 hours. What is the probability that the average lifetime of 64 of these lightbulbs is more than 9100 hours? [Hint: Use the Central Limit Theorem.] SHOW YOUR WORK. Paragraph BIU A + v CAFOA DII F3 F4 FS prt sc F10 home end F12 F6 F7 insert F8 F9 F11 %24 III liliGiven the Cumulative Distribution Function (CDF) of X. Find the variance and the standard deviation of X F(x) = 0 for x < -2 3 for – 2Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,