45. A type of lightbulb is labelled as having an average lifetime of 1000 hours. It is reasonable to model the probability of failure of these lightbulbs with an exponential density function with p 1000. What is the probability a lightbulb lasts longer than 800 hours? A) el B) C) es D) 1-e¹ E) None of the above.
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- 2. The number of minutes a flight from Phoenix to Tucson is early or late is a random variable whose 1 (36– x*) for-6Question 34. Let X be a random variable with probability density function Sžr², re (0,3), f(r) = else. Which of the following statements are correct? I a) The expected value of X is . b) The probability of X < 1 is . c) The probability of X € [0,0.5] is . d) The probability of X = 1 is zero.1. The region formed by a probability density function represented by a nonconstant linear function is _______________. a. Triangular b. Trapezoidal c. None of these d. Rectangular 2. The following is true about probability density function EXCEPT _______. a. The function is always nonnegative. b. None of these c. The probability of an individual value of random variable is zero. d. The total area under the graph is 1. 3. The region formed by the probability density function representing a continuous uniform distribution is ____________. a. Triangular b. Rectangular c. Slanted Line Segment d. Horizontal Line SegmentBalls are numbered 1 through 10 (including 1 and 10) in an urn. 3 are drawn simultaneously and at random. If X is 3 times the number of even balls drawn minus 2 times the number of odd balls drawn, how many distinct values for X are there? Find the probability density function of X?Question 5: The length of a wire used in an electrical component is supposed to be 10cm. The machine that stamps out the parts hasn't been recalibrated recently and is making the wires (10 + y) cm long where y varies from wire to wire according to the probability density function 3 fW) = 38 y(1 + y) 0The lifetime T(in years) of a device is given by the probability density function in the picture below. Two students are asked to find t=L. Please help find which student had the right setup to find L with work. Either one, both, or neither.Q.5). A manufacturer guarantees a product for 1 year. The time to failure of the product after it is sold is given by the probability density function S.01e-01t f(t) = if t z0 otherwise where t is time in months. What is the probability that a buyer chosen at random will have a product failure (A) During the warranty period? (B) During the second year after purchase? EndQuestion 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.Question 2 The probability density function of the reliability of a piece of equipment is given by: a x)= a(162 – x²³) (x)=(a/1 16-x³ 0Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON