Advertisements
Advertisements
प्रश्न
The probability function of a random variable X is given by
p(x) = `{{:(1/4",", "for" x = - 2),(1/4",", "for" x = 0),(1/2",", "for" x = 10),(0",", "elsewhere"):}`
Evaluate the following probabilities
P(X ≤ 0)
Advertisements
उत्तर
| X | – 2 | 0 | 10 |
| PX = x) | `1/4` | `1/4` | `1/2` |
P(x ≤ 0) = P( x = – 2) + P(x = 0)
= `1/4+ 1/4`
= `2/4`
= `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
Construct cumulative distribution function for the given probability distribution.
| X | 0 | 1 | 2 | 3 |
| P(X = x) | 0.3 | 0. | 0.4 | 0.1 |
Let X be a discrete random variable with the following p.m.f
`"P"(x) = {{:(0.3, "for" x = 3),(0.2, "for" x = 5),(0.3, "for" x = 8),(0.2, "for" x = 10),(0, "otherwise"):}`
Find and plot the c.d.f. of X.
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
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 |
Find k
Define dicrete random Variable
Choose the correct alternative:
If we have f(x) = 2x, 0 ≤ x ≤ 1, then f(x) is a
Choose the correct alternative:
A variable which can assume finite or countably infinite number of values is known as
Let X be a random variable with a cumulative distribution function.
F(x) = `{{:(0",", "if" x < 0),(x/8",", "if" 0 ≤ x ≤ 1),(1/4 + x/8",", "if" 1 ≤ x ≤ 2),(3/4 + x/12",", "if" 2 ≤ x < 3),(1",", "for" 3 ≤ x):}`
Is X a discrete random variable? Justify your answer
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)
