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A random variable X has its probability function given by 1 T2 T f(x) 0.30 0.10 C L 0.2 0.4c a) [3.5 marks] Find c and F(x), the cumulative distribution function for X (for all real values of X).

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

Q5. Let (Ω, F , P) be a probability space. Let λ > 0 be some constant.

  1. (a)  Give the definition of a random variable X on R ∪ {−∞, +∞}.

  2. (b)  Define the distribution function FX for the RV X.

[6 marks]

[1 marks]

[1 marks] (c) Suppose that Y is a RV on R ∪ {−∞, +∞} with distribution function given by

􏰄3 −1e−λy (y≥0)

[6 marks]

page1image62001664 page1image62003968

FY (y) = 4 2 1

(y < 0).
For any a < b, determine P(Y > a), and P(Y ∈ (a, b]). [3 marks]

  1. (d)  By noting {Y < b} = ∪n∈N{Y ≤ b − 1 } and using Continuity of Probability, n

    find P(Y < b). Similarly, find P(Y < ∞) and P(Y = −∞). [4 marks]

  2. (e)  Is Y either a discrete RV, or a continuous RV, or a mixture of both? Explain

    your answer. [1 marks]

For a continuous random variable x, the probability density function f(x) represents
 
a. the probability at a given value of x
 
b. the area under the curve at x
 
c. the probability at a given value of x and the area under the curve at x are correct answers.
 
d. the height of the function at x
In the following probability distribution, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in.
 
     x      P(x) 0      0.272     10.575      20.121      30.027     40.004      50.001 
 
(a) Verify that this is a discrete probability distribution.
(b) Draw a graph of the probability distribution. Describe the shape of the distribution.
(c) Compute and interpret the mean of the random variable X.
(d) Compute the standard deviation of the random variable X.
(e) What is the probability that a randomly selected individual 15 years or older was involved in tow marriages?
(f) What is the probability that a randomly selected individual 15 years or older was involved in at least two marriges?

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