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- Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?Suppose that Xis a continuous unknown with -4< X< 4 having PDF denoted fsatisfying f ( x ) = c ( 16 − x^2 ) ,for -4< x< 4. Here c is a positive normalizing constant. What is the value of c?Suppose X is exponentially distributed with mean 2. Let Y = eX. What is the density function of Y?
- The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2P(x)=12e-x/2for x in [0,∞)[0,∞). Find the probability that a randomly selected laptop battery will last between 3 and 8 years?I was calculating a conditional density function and I got an answer of 2x+3y all over 2x+3/2. When I checked the answer, it was 4x+6y all over 4x+3. Those two answers are the same, but my question is--is there some protocol as far as what is proper form to express an answer in when dealing with density functions?Suppose that the lifetime X (in hours) of a certain type of flashlight battery is a random variable on the interval 30 ≤ x ≤ 50 with density function f(x) = 1/20, 30 ≤ x ≤ 50. Find the probability that a battery selected at random will last at least 35 hours.
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