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- Let X be a continuous random variable, and let K be a countable set. Prove that Pr(X E K) = 0. Use this to explain why X can't also be a discrete random variable.An environmental engineer collected 10 moss and 10 lichen specimens. The engineer instructs a laboratory intern to randomly select 15 of the specimens. The probability mass function of the number of lichen specimens selected at random is: a) H (x; 15; 10; 20) b) P (x; 10) c) Bnegative (x, 10, 0.666) d) B (x, 10, 0.666)A kindergarten class consists of 12 boys and 4 girls. The children are arranged from tallest to shortest. Assume that all 16! rankings are equally likely, and no two children are the exactly the same height. let the random variable X be the rank of the second tallest boy. assume that the tallest person in the class is rank 1. (a) find f(x) (b) Calculate E[X] and V[X]
- 1.) The amount of time an air-conditioning technician to repair a unit is in between 1.9 and 5 hours which is found to be uniformly distributed. Let x be the time needed to fix an A/C unit. b.) Find the probability that a randomly selected A/C unit repair requires less than 3.5 hours?Let random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :İf X follows the Poisson probability law such that P (xr 1) = P (x = 2). then ind the probability of 4 successes.
- Let X equal the IQ of a randomly selected American. Assume X ~ N( μ μ {"version":"1.1","math":"μ"} =100, σ σ {"version":"1.1","math":"σ"} =4). What is the probability that a randomly selected American has an IQ below 90?İf X follows the Poisson probability law such that P (xr 1) = P (x = 2). then ind the probability of 4 successes.The random variable x is N(10,1). Find f(x(x-10)²<4).