Advertisements
Advertisements
प्रश्न
The p.d.f. of X is defined as
f(x) = `{{:("k"",", "for" 0 < x ≤ 4),(0",", "otherwise"):}`
Find the value of k and also find P(2 ≤ X ≤ 4)
Advertisements
उत्तर
Let X and a random variable if a Probability density function
`int_(-oo)^oo "f"(x) "d"x` = 1
Here `int_0^4 "f"(x) "d"x` = 1
`int_0^4 "k" "d"x` = 1
⇒ `"k"[x]_0^4` = 1
`"k"[4 - 0]` = 1
⇒ 4k = 1
∴ k = `1/4`
P(2 ≤ x ≤ 4) = `int_2^4 "f"(x) "d"`
= `int_2^4 "kd"x`
= `int_2^4 1/4 "d"x`
= `1/4 int_2^4 "d"x`
= `1/4 [x]_2^4`
= `1/4 [4 - 2]`
= `1/4 [2]`
= `1/2`
APPEARS IN
संबंधित प्रश्न
Two balls are chosen randomly from an urn containing 6 red and 8 black balls. Suppose that we win ₹ 15 for each red ball selected and we lose ₹ 10 for each black ball selected. X denotes the winning amount, then find the values of X and number of points in its inverse images
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
Define dicrete random Variable
Explain the terms probability Mass function
State the properties of distribution function.
Choose the correct alternative:
If c is a constant, then E(c) is
Choose the correct alternative:
If the random variable takes negative values, then the negative values will have
Choose the correct alternative:
If we have f(x) = 2x, 0 ≤ x ≤ 1, then f(x) is a
Choose the correct alternative:
A set of numerical values assigned to a sample space is called
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
