By specifying its probability function,
px, and a random variable X with cumulative distribution function:
F
X
(
t
) =
8
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>
>
>
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>
>
>
>
<
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:
0
; t <
3
1
=
3
;
3
t <
4
1
=
2
;
4
t <
5
2
=
3
;
5
t <
6
1
; t
6
Calculate Pr(3
X
4).
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By specifying its probability function,pX, and a random variable X with cumulative distribution function:
Cumulative distribution function The probability distribution of a discrete random variable X is given below: Value x of X P(x-x) 0.24 0.11 -2 0.26 0.11 Let Fx be the cumulative distribution function of X. Compute the following: X 5 ? 18+ (-2) - Px (-4) = 0
PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks b) The life expectancy (in days) of a mechanical system has a probability density write down equations for the cumulative distribution C(x) and the survival distribution Px). State a relationship between them. function f(x)=1/x, for x21, and f(x)=0 for x <1. i Find the probability that the system lasts between 0 and I day.2 marks i) Find the probability that the system lasts between...
Suppose that X is a continuous random variable with density pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1. (a) Find C so that pX is a probability density function. (b) Find the cumulative distribution of X. (c) Calculate the probability that X ∈ (0.1, 0.9). (d) Calculate the mean and the variance of X. 9.) Suppose that X is a continuous random variable with density C(1x) if E...
9.) Suppose that X is a continuous random variable with density C(1- if [0,1] px(x) ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function. (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distribution function if x<0 F(x)ax2 0.1x if osxs 20 if x> 20 0 Find 1) the coefficient a; 2) P 10); 3) P(X<30). 2. The result of some measurement X is normally distributed with parameters 184 and 8. Compute the probability that variable X takes value from interval (170;180) at least once in 5 experiments 3. Two independent random variables X...
Exercise 3.37. Suppose random variable X has a cumulative distribution function F(x) = 1+r) 720 x < 0. (a) Find the probability density function of X. (b) Calculate P{2 < X <3}. (c) Calculate E[(1 + x){e-2X].
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
2) Consider a random variable with the following probability distribution: P(X-0)-0., Px-1)-0.2, PX-2)-0.3, PX-3) -0.3, and PX-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 values. How do these summary measures compare to the...
2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2 0.5 ェ<2, 2-1<5.7, 5.7-1 6.5, 6.5 <エ<8.5, F(z)= 18.5 エ a) Find the probability mass function of X b) Find the probabilities P(x>5), P(4<X 6x> 5) c) If E(X) = 5.76, find c.