Use your pdf graph to find the cdf and graph it. Briefly explain your methods. Hint: you might calculate the cdf for yearly intervals.
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- Martian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after planting until a Martian potato sprouts. Then X has the following probability density function: f(x)= 2/7e−x + 3/14e−x/2 + 1/14e−x/4 for 0 ≤ x ≤ ∞ and 0 otherwise. f) What is the variance of X? g) What is the standard deviation of X? h) What is the probability that X is more than 2 standard deviations above its expected value?DHL usually gives its customer a 60-minute window in which it expects home deliveries to be delivered. An independent consultant estimates that the final delivery time within the window is a delivery that follows the following condensation function:a. Draw the density function of the event. b. What is the expected value of the transaction? c. What is the variance of the event?DHL usually gives its customer a 60-minute window in which it expects home deliveries to be delivered. An independent consultant estimates that the final delivery time within the window is a delivery that follows the following condensation function: a. Draw the density function of the event. b. What is the expected value of the transaction? c. What is the variance of the event?
- Martian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after planting until a Martian potato sprouts. Then X has the following probability density function: f(x)= 2/7e−x + 3/14e−x/2 + 1/14e−x/4 for 0 ≤ x ≤ ∞ and 0 otherwise. d) What is the expected value of X (E(X))? e) What is the expected value of X2 ? f) What is the variance of X?Construct a relative frequency marginal distribution. x1 x2 x3 Relative frequency marginal distribution y1 30 25 30 enter your response here y2 30 15 50 enter your response here Relative frequency marginal distribution enter your response here enter your response here enter your response here 1 (Round to three decimal places as needed.)2. The average American spends 4.4 hours per day watching television. Supposethe standard deviation is 2.1 hours a. Use Chebyshev’s theorem to calculate the percentage of individuals watchingbetween 0.2 and 8.6 hours per day.b. Suppose the watching television time follows a normal distribution. Sketch thisnormal density curve. Label the points one, two, and three standarddeviations from the mean.c. Use the empirical rule to calculate the percentage of individuals watchingbetween 0.2 and 8.6 hours per day.
- Martian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after planting until a Martian potato sprouts. Then X has the following probability density function: f(x)= 2/7e−x + 3/14e−x/2 + 1/14e−x/4 for 0 ≤ x ≤ ∞ and 0 otherwise. g) What is the standard deviation of X? h) What is the probability that X is more than 2 standard deviations above its expected value? i) What is the expected value of X4 ?Let X be physical distance, measured in inches, from its anchoring point where a bicycle spoke will snap. Then X has the following probability density function: f(x)= (6/169)x(1-x/13) for 0 ≤ x ≤ 13 and 0 otherwise. a)What is the expected value of X (E(X))? b)What is the expected value of X2? c)What is the variance of X? d) What is the standard deviation of X? e)What is the probability that X is less than its expected value? f)What is the expected value of X0.6?Battery 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?
- I have true false questions.(There is no need to explain, it is enough just to write true or false.) 1)If the probability density functions of the independent random variables X and Y are defined in the set A = {(x, y): 0 <x <1, 0 <y <1}, then the variables Z1 and Z2, defined as Z1 = X-Y and Z2 = Y, are also independent. 2)The average of the grades taken in an exam is thought to come from the normal distribution with μ and variance σ2. If a student's grade is between μ and μ + σ, the student's grade is B. Accordingly, the student's probability of getting a B grade is equal to the probability P (0 <Z <1).The amount of coffee poured from a dispenser into a glassobeys the normal law whose average is 300 mL and the deviationtype 5 mL.a) What proportion of the glasses of coffee served by this dispenser contain less than 292 mL of coffee?b) If the glasses have a maximum capacity of 310 mL, whatproportion of glasses overflowing when usedwith this distributor?c) What should be the capacity of the glasses so that only 1% of them overflow when used?with this distributor?Find the expected value of the random variable Y whose probability density is given by f( y) = 1/8 (y + 1) for 2 < y < 4 , 0 for elsewhere