I1. If X has the distribution function for x<1 for 1sx<4 F(x) for 4 sx <6 for 6sx<10 for x 10 find (a) P(2< xs 6); (b) P(X = 4); (c) the probability distribution of X. %3D

Q: A continuous random variable X has the p.d.f. f(x) = (a) Find the mean of X. (b) Find the variance…

A: The probability density function of Xf(x)=1/2e-|x|    for  0                        otherwiseWe have…

Q: a. What is probability that a randomly selected employee has a commute of less than one hour and…

A: Here given joint pdf of X and Y

Q: The graph of a continuous probability distribution cannot have y-values larger than 1.

A: Given that   The graph of a continuous probability distribution cannot have y-values larger than 1.…

Q: For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is…

A:

Q: Suppose X = time to wait for a cab and you know you're going to wait at least 6 minutes, but no more…

A: Given: X follows Uniform distribution in [ 6 , 10]

Q: 16. (BONUS) Use Chebyshev's Theorem to find the following probability. If u = 5, o? = 9. Assume x…

A:

Q: 5. An automobile dealer has found that X, the number of cars customers buy each week, follows the…

A: The given function is: f(x)=kx2x!,x=1,2,3,40,       Otherwise

Q: (a) Determine the value of k for which f(x) is a legitimate pdf. 5 (b) Obtain the cumulative…

A: Here as per policy i have calculated 3 subparts , plz repost for Remaining . Here given, "Time…

Q: 2. Let f(x) = 3x(x² − 1)(x³ + 2x + 3) (a) Use distribution to expand the function. (b) Use the rules…

A:

Q: 2. Consider the function Fx(x) = 0 E. x 2. (a) State the 4 properties of a distribution function.

A: Given: FX(x)= 0                               x&lt;0=x2…

Q: Why the probability P(X=x)=0, for a continuous variable,?

A: Given info: The probability P(X=x)=0, for a continuous variable

Q: Suppose that the lifetime in years, X,  of a type of electrical switch follows the distribution…

A: Exponential distribution: A continuous random variable X is said to follow exponential distribution…

Q: Explain the steps if you can

A: a.)x01234P(x).45.21.13.12.09F(x) 0.45 0.660.790.911b.) E(X) = 1.19Explanation:a.) F(x) = P(X≤x)(To…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!