If the probability distribution of a random variable X is given by - X -xi- - PX-xi- 2 k - 2 k 2 33 k43 k 4 kWrite the value of k-

We know that the sum of probabilities in a nbsp;probability distribution is always 1. there4; P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) = 1 #8658; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Classical Definition of Probability

If the probab...

Question

If the probability distribution of a random variable X is given by

X = x_i : 1 2 3 4

P (X = x_i) : 2k 4k 3k k

Write the value of k.

Open in App

Solution

We know that the sum of probabilities in a probability distribution is always 1.

∴ P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) = 1

$\Rightarrow 2 k + 4 k + 3 k + k = 1 \Rightarrow 10 k = 1 \Rightarrow k = \frac{1}{10} = 0.1$

Suggest Corrections

Similar questions

Q. The probability distribution of a random variable X is given below

$X = x_{i}$	$P (X = x_{i})$
$1$	k
$2$	$2 k$
$3$	$3 k$
$4$	$4 k$
$5$	$5 k$

Find the value of k and the mean and variance of X.

Q. If the probability distribution of a random variable X is as given below:

X = x_i :	1	2	3	4
P (X = x_i) :	c	2c	4c	4c

Write the value of P (X ≤ 2).

Q. If a random variable

x

has the following probability distribution

X = x_{i} : 0123

P (X = x_{i}) : 2 K^{2}, 3 K^{2}, 5 K^{2}, 6 K^{2}

then the value of

K

Q. The variance of the random variable

x

whose probability distribution is given by

X = x_{i} : - 1, 0, + 1

p (X = x_{i}) : 0.4, 0.2, 0.4

Q. A random variable has the following probability distribution:

X = x_i :	1	2	3	4
P (X = x_i) :	k	2k	3k	4k

Write the value of P (X ≥ 3).

Join BYJU'S Learning Program

If the probability distribution of a random variable X is given by X = xi : 1 2 3 4 P (X = xi) : 2k 4k 3k k Write the value of k.

We know that the sum of probabilities in a probability distribution is always 1. ∴ P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) = 1 ⇒2k+4k+3k+k=1⇒10k=1⇒k=110=0.1

If the probability distribution of a random variable X is given by

X = x_i : 1 2 3 4

P (X = x_i) : 2k 4k 3k k

Write the value of k.

We know that the sum of probabilities in a probability distribution is always 1.

∴ P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) = 1

$\Rightarrow 2 k + 4 k + 3 k + k = 1 \Rightarrow 10 k = 1 \Rightarrow k = \frac{1}{10} = 0.1$