b) A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb inyears is given by(ve-tof(y)=0

Given that,A technician discovered that the cumulative distribution (CDF) of thelifespan of bulb in…

Answered: A technician discovered that the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider an electronic component with a lifetime denoted by a random variable T which is modelled by an exponential distribution with a parameter of average lifetime B = 5. Part A: Exponential Distribution Write the probability that a component is still working after 5 years, as an expression: P(T > 5) = | dt Use t for T e() for exponential function ()! for factorial ( )*( ) for exponents • Help entering equations Part B: Probability Write the probability that a component is still working after 5 years, numerically: P(T > 5) = • Help entering equations Part C: Binomial Distribution Let X be the random variable representing the number of components that are still working after 5 years. Write the binomial distribution for at least 3 components that are still working, as an expression: P(X 2 3) = Use p for parameter p x for the value of the random variable X e() for exponential function C(n,x) for combination of "x out of n" (O! for factorial (O*) for exponents • Help entering equations…
A model for normal human body temperature, X, when measured orally in °F, is that it is normally distributed, X ~ N (98.2,0.5184). (i) According to the model, what proportion of people have a normal body temperature of 99 °F or more? (ii) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. (iii) Let W denote normal human body temperature, when measured orally in °C. Given that W = (X - 32) and X ~ N(98.2,0.5184), what is the distribution of W? (iv) According to the model that you just derived for W, what proportion of people have a normal body temperature of between 36 °C and 36.8 °C?
True or False? 1/n∑(Xi − X)^2 is an asymptotically unbiased estimator for the variance of X.
Let Y be the present value random variable of a 10-year term annuity-due of 1 issued at an individual (35). Calculate its actuarial present value if (a) Mortality follows De Moivre's Law with w = 100. (b) 8 = 0.05.
Write the following distributions in the form of the exponential form: (i) Poisson P(0); (ii) Geometric G(0); (iii) Gamma I'(a, B).
'5 7 Given f(x) dx : = 12 and f(x) dx = 4, evaluate %D 7. (a) f(x) dx. 0. (b) / f(x) dx. '5 (c) f(x) dx. (d) 2f(x) dx.
An accident-prone motorist has two tragic accidents with two weeks between rooms. The 'waiting time' (measured in days) between two accidents can be approximately approximated as exponentially distributed with unknown expected value µ. Determine a 90% condensation interval for µ. Please explin so I understand to ba able to solve similar kind of questions..
The time until a chemical reaction is complete (in milliseconds) is approximated by cumulative distribution function F(2) = { ,"ani 0lz The probability that a reaction completes within 400 milliseconds is
Following equation is given Y= (x+5)^3 + x^2 +10x What is the expected value of Y? Given E{X} = 4 E{x^2} = 9 E{x^3} =12 Explain Briefly
If I had a series of data X = (x₁+x₂+x₂+ 1 2 +xN} I would have a mean and standard deviation, and s X If I subtracted 3 from every observation in the data series, X, which of the following would happen? The mean of X will increase by 3 The mean of X will decrease by 3 The standard deviation of X will be three times as large The standard deviation of X will be one third as large 3 ...
The expectation of X, which is also known as the mean or average, is E(X) = 7 and the Variance of X is var(X) =4. Using the equation Y = 11X + 81. What are the expected value E(Y), variance VAR(Y), and standard deviation SD(Y) of this expression.

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A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by ye to f(y)= 0