Verify that the following function is a cumulative distribution function. 0 F(x)=0.5 Round your answers to 1 decimal place (e.g. 98.7). Determine: P(1 ≤x≤2) = 1 x < 1 1
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- If X has the exponential distribution given by f(x) =0.5 e−0.5x, x > 0, find the probability that x > 1.The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)=1/162(x-3)^2(x+6) for 0 < x < 6What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?Answer to four decimal places What is the probability of a widget being made later than 1.3 s?Answer to four decimal placesLet X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1 Compute P(X≤4) and P(2≤X≤5)
- If X has the exponential distribution given by: f(x) = 4*(1 - x/2); 1 ≤ x ≤ 2. Find E(x).Verify that the following function is cumulative distribution function, and determine the probability mass function and the requested probabilities. F(x) ={ 0, X < 1 0.5, 1 ≤ x < 3 1, 3 < ? } (a)P(X≤3) (b)P(X ≤2) (c)P(1≤X≤2) (d)P(X>2)If X has the exponential distribution given by: f(x) = 4*(1 - x/2); 1 ≤ x ≤ 2. Find the probability that 1.2 < x < 1.6.
- The probability density function of X, the lifetime of a certain device in months, is given by f(x)=6/(x^2) if x > 6 and f(x) = 0 if x < 6. Find P(X > 50). Also, what is the cumulative distribution function of X on x > 6?Derive a general expression for the variance of net future loss Var(L) with a constant force of interest δ under each of the following models:i. μ_x(t) = μii. μ_x(t) = 1/(ω-x)Let X be the number of microorganisms in a proliferation culture whose Function of Cumulative Distribution (fda) is given by: F(x) = 1 − e−λx, for x > 0. What is the value of λ such that P(X ≥ 10.14) = 0.8
