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- Question * Given X be the life time of a bulb having a probability density function f(x) =-e for x>0 and 0 elsewhere. The mean life time of the bulbs is equal to: %3D O 1/2 O None of these O 1/4 Question* Let X and Y be two independent continuous random variables with marginal distributionansewr D and E onlyThe time that a butterfly lives after emerging from its chrysalis can be modelled by a random variable T, the model here taking the probability that a butterfly survives for more than t days as 36 P(T >t) GE7, t>0. (6+t)² » For these problems, please ensure your answers are accurate to within 3 decimals. Part a) What is the probability that a butterfly will die within 6 days of emerging? Part b) If a large number of butterflies emerge on the same day, after how many days would you expect only 6 % to be alive? Part c) Calculate the mean lifetime of a butterfly after emerging from its chrysalis.
- Question * Let X and Y be two continuous random variables with joint probability density function given by: (х. у)%3D (8xy, 09/10 Question * If the probability density function of random variable X is given by: - 1)(2- x), 0, 15 xS 2; otherwise. The value of k is equal to: None of these 3/2 7. 6. Question *نقطتان )2) Q10) If you know that is the following function is joint probability density function, * ?what is the value of t S9xy 0ASAP4. The probability density function of a continuous random variable } is: (1 + x) f(x) = if -1 < x < 0 3 (3 - 2x) if 0 ≤ x < ₂ < ²³/ 15 Derive the distribution function of ! (Solution: 0, if x≤e1 if-1For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfishSEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON