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- Find x?e**dx Sx²If time between two ATM transaction is exponentially distributed with Lambda = 1 minutes. find the probability that the time between two transactions is more than 0.79 minutes. (answer to three decimal places)Find the mean value of x³+x²+x y = Over the range - 1Determine moment generation function of the Exponential distribution.The amount of time required to serve a customer at a bank has an exponential density function with a mean of 3 minutes. Find the probability that a customer is served in less than 2 minutes and also find the probability that serving a customer will require more than 5 minutes.For a continuous pdf, the probability of an exact value can be found . Is this true or false ? And example ?The life X (in hours) of a battery in constant use is a random variable with exponential density. What is the probability that the battery will last more than 12 hours (h) if the average life is 8 h?Assume that the time it takes for bacterial growth on a dairy product after it is taken out of fridge follows an Exponential distribution with a mean of 10 minutes. What is the probability that bacterial growth will not happen in 15 minutes if the dairy product has already been out of the fridge for 10 minutes?Suppose that the length of long distance phone calls, mea- sured in minutes, is known to have an exponential distribution with the average length of a call equal to 15 minutes. Find the CDF.A company that makes rice cookers performed some quality control experiments, and found that the number of years before their products would fail has the following probability density function, as described in Desmos demonstration below. Untitled Graph 10 Probability density function 5- 3 00} 4 k=2 10 Show P(X < k) -5 11 powered by What is the probability that a random rice cooker produced by the company would fail between 4.4 and 6.2 years of usage? (Your answer should be a decimal. Round to 4 decimal places if necessary.)The life X (in years) of a voltage regulator of a car has the pdf: X 3 - (-/-)². 3x2 73 0≤x≤∞ What is the probability that this regulator will last at least 7 years? Give your answer to 3 decimal places and show working.ASAP when theq=5 /p =5