Advertisements
Advertisements
Question
The discrete random variable X has the probability function
| X | 1 | 2 | 3 | 4 |
| P(X = x) | k | 2k | 3k | 4k |
Show that k = 0 1
Solution
P(x = 1) = k
p(x = 2) = 2k
p(x = 3) = 3k
P(x = 4) = 4k
Since P(X = x) is a probability Mass function
`sum_(x = 1)^4` P(X = x) = 1
`sum_("i" = 1)^oo` P(xi) = 1
p(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) = 1
P(x = 1) + P(x = = 2) + P(x = 3) + P(x = 4) = 1
k + 2k + 3k + 4k = 1
10k = 1
k = `1/10`
∴ k = 0.1
APPEARS IN
RELATED QUESTIONS
Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images
The discrete random variable X has the probability function.
| Value of X = x |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
If P(X ≤ x) > `1/2`, then find the minimum value of x.
The length of time (in minutes) that a certain person speaks on the telephone is found to be random phenomenon, with a probability function specified by the probability density function f(x) as
f(x) = `{{:("Ae"^((-x)/5)",", "for" x ≥ 0),(0",", "otherwise"):}`
What is the probability that the number of minutes that person will talk over the phone is (i) more than 10 minutes, (ii) less than 5 minutes and (iii) between 5 and 10 minutes
Explain what are the types of random variable?
Distinguish between discrete and continuous random variables.
Choose the correct alternative:
If c is a constant, then E(c) is
Choose the correct alternative:
Which one is not an example of random experiment?
Choose the correct alternative:
The probability function of a random variable is defined as
| X = x | – 1 | – 2 | 0 | 1 | 2 |
| P(x) | k | 2k | 3k | 4k | 5k |
Then k is equal to
Choose the correct alternative:
A discrete probability function p(x) is always
The probability density function of a continuous random variable X is
f(x) = `{{:("a" + "b"x^2",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
where a and b are some constants. Find Var(X)
