(f(x) is a probability density function?(=0.111 (0Q4/ the value of the constant which makes the function 3>x>00.wB) and0.321 (1c) 0.5

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A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(b) The probability density of a function is given by p(x) from x = 1 to x = 4. That is 62 x3 dx = 1 62 P(x) dx = - 00 Determine the value of the standard deviation.
Consider the following exponential probability density function. 1 -x/4 f(x) = -e (a) Write the formula for P(x ≤ xo). for x ≥ 0 (b) Find P(x ≤ 2). (Round your answer to four decimal places.) (c) Find P(x ≥ 4). (Round your answer to four decimal places.) 0.3679 (d) Find P(x ≤ 5). (Round your answer to four decimal places.) (e) Find P(2 ≤ x ≤ 5). (Round your answer to four decimal places.)
The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…
Şe x² f(x)=cis a probability density function? 0.111 (2 c) 0.5 /The value of the constant, which makes the function 3 >> 00w father 0.321 (
Consider the probability density function f(x) = 1.5x² for -1 ≤x≤ 1. What is P(X > 0)? O a. 0 b. 0.125 c. 0.25 O d. 0.5
Determine whether the following function is a probability density function. f(x) = x, 0sxs8 32 Is the function f(x) a probability density function? No Yes
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Consider a constant function: f(x)= c; a ≤ x ≤ b Suppose that the function represents a probability density function and c<1 , which of the following is true? a. |a−b|<0 b. |a−b|<1 c. |a−b|>1 d. |a−b|=1
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Consider the following constant function: f(x) = 3/4 If this function represents a probability density function, which of the following can be a set of realized values? A. 2/3 ≤ x ≤ 2 B. 1/4 ≤ x ≤ 1 C. 3 ≤ x ≤ 4 D. 1/2 ≤ x ≤ 3/2
[1] The probability density function of a random variable X is SC(x + 4), -4 4.
Consider the pdf g(y) = .06(y² + 1) on -2 ≤ y ≤ 3. (a) Calculate the probability that P(Y > 1). (b) Calculate E[Y]. (c) Calculate Var(Y).

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(f(x) is a probability density function? (= 0.111 ( Q4/ the value of the constant which makes the function 3>x>0 0.w B) and 0.321 ( c) 0.5