Solution: μ = 10
The standard deviation of X is σ = μ
The parameter of the exponential distribution of X is λ = 1/μ
=> option B. P(X < 7) = 0.5034
=> option B. P(12 < x < 20) = 0.1659
6. The exponential distribution Consider the random variable x that follows an exponential distribution, with p...
Using Excel - normal probabilities Consider the random variable x that follows a normal distribution, with a mean of μ = 54 and a standard deviation of σ = 4. You will select some of your answers to the questions that follow in this sample Excel spreadsheet: A B 1 P(x < 50.5) 2 P(49 < x < 51) In cell B1 of the sample spreadsheet, select the correct Excel formula for computing the probability that x is less than...
A discrete random variable X follows the geometric distribution
with parameter p, written X ∼ Geom(p), if its distribution function
is
A discrete random variable X follows the geometric distribution with parameter p, written X Geom(p), if its distribution function is 1x(z) = p(1-P)"-1, ze(1, 2, 3, ). The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that fx(x) is indeed a probability...
2) Consider a random variable with the following probability distribution: P(X = 0) = 0.1, P(X=1) =0.2, P(X=2) = 0.3, P(X=3) = 0.3, and P(X=4)= 0.1. A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated...
6.4.32 A random variable follows the continuous uniform distribution between 160 and 360. Calculate the following quantities for the distribution. a)P(220 less than or equal to x less than or equal to 330) b)P(160 less than or equal to x less than or equal to 280) c)P(x>180) d) What are the mean and standard deviation of this distribution? a)P(220 less than or equal to x less than or equal to 330)= (Type an integer or decimal rounded to three decimal...
please help with all.
In the following probability distribution, the random variable x represents the number of activities a parent of a 6th-to 8th grade student is involved in. Complete parts (a) through (1) below. * 1 0 1 2 3 4 5 P(x) 0.269 0 206 0.224 0.239 0.062 (a) Verify that this is a discrete probability distribution This is a discrete probability distribution because the sum of the probabilities is and each probability is (6) Graph the discrete...
Multiple Choice Question Let random variable X follows an exponential distribution with probability density function fx(x) = 0.5 exp(-x/2), x > 0. Suppose that {X1, ..., X81} is i.i.d random sample from distribution of X. Approximate the probability of P(X1 +...+X31 > 170). A. 0.67 B. 0.16 C. 0.33 D. 0.95 E. none of the preceding
Let x be the binomial random variable with n=10 and p = 9 a. Find P(x = 8) and create a cumulative probability table for the distribution. b. Find P( x is less than or equal to 7) and P(x is greater than 7) c. Find the mean, u, the standard deviation, o, and the variance. d. Does the Empirical rule work on this distribution for data that is within one, two or three standard deviations of the mean? Explain....
6.33 Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 28 and 34 b. between 20 and 35 6.34 Let x be a continuous random variable that has a normal distribution with a mean of 30 and a stan- dard deviation of 2. Find the probability that x assumes a value a. between 29 and 35 b....
A random variable follows the normal probability distribution with a mean of 80 and a standard deviation of 20. Determine the probability for a randomly selected value from this population in parts a through d below. a. is less than 90 b. is less than 65 c. is more than 110 d. is more than 40.
A random variable follows the continuous uniform distribution between 30 and 120 a) Calculate the probability below for the distribution. P(60less than or equals≤xless than or equals≤90) b) What are the mean and standard deviation of this distribution? wo neng kan jian wen ti