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- The failure time (T) of an electronic circuit board follows exponentially distribution with failure rate λ = 10−4/h. What is the probability that (i) it will fail before 1000 h? (ii) it will survive at least 10,000 h ? (iii) it will fail between 1000 and 10,000 h? (iv)Determine the mean time to failure. .EX#2: Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 4. Find the probability between x = 25 and x = 32.The lifetime (in hours ) of a semiconductor laser has a lognormal distribution with theta = 10 and omega = 1.5 Determine the following in parts (a) and (b): a) Probability the lifetime is less than 1000 hours ? b) Probability the lifetime is less than 11000 hours given that it is more than 10000 hours?
- The random variable X is exponentially distributed, where X represents the waiting time to see a shooting star during a meteor shower. If X has an average value of 45 seconds, what are the parameters of the exponential distribution?Suppose that the time-to-failure of a system has a distribution with the following pdf: f(x) = 0.1e^(-0.1x) What is the probability that the failure occurs between 5 and 20? a). 0.23 b). 0.47 c). 0.088 d). 0The orders from n= 100 customers for wooden panels of various thickness (X) are summarized as follows: *refer from the table attached* Determine the probability mass function X and plot f(x).
- 4) Considey molecules cnd 100 10 cells of equal energy. Find log. energy most probabile and ii the wfor j the distribution least probable distribution.For a loss X with exponential distribution with parameters mean , what can you conclude about it's mean excess loss? Show the proofing process of your conclusion above.IfXhas exponential distribution with mean 1 (X~EXP(1)), then P(X>2|X>1)equals to
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