A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X = 3) = 2P(X = 1) and

Q: A random variable $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X = 3) = 2P(X = 1)$ and $P(X = 2) = 0.3,$ then $P(X = 0)$ is:

Let: $P(X = 0) = m$ $P(X = 1) = k$ Now, $P(X = 3) = 2k$ $x_i$ $p_i$ $p_ix_i$ $0$ $m$ $0$ $1$ $k$ $k$ $2$ $0.3$ $0.6$ $3$ $2k$ $6k$ Mean $=\sum\text{p}_\text{i}\text{x}_\text{i}$ $\Rightarrow 0 + k + 0.6 + 6k = 1.3$ $\Rightarrow 7k = 1.6 - 0.6$ $\Rightarrow\text{k}=\frac{0.7}{7}$ $\Rightarrow 0.1$ We know that the sum of probabilities in a probability distribution is always $1$. $\therefore P(X = 0) + P(X = 1) + P(X = 3) = 1$ $\Rightarrow m + 0.1 + 0.3 + 0.2 = 1$ $\Rightarrow m + 0.6 = 1$ $\Rightarrow m = 0.4$

M.C.Q (1 Marks)

GSEB - English Medium

A random variable $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X = 3) = 2P(X = 1)$ and $P(X = 2) = 0.3,$ then $P(X = 0)$ is:

A$0.1$
B$0.2$
C$0.3$
D$0.4$

STD 12 Science
Maths
Probability
Exemplar

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

X:	0	1	2	3	4	5	6	7	8
P(X):	a	3a	5a	7a	9a	11a	13a	15a	17a

$x_i$	$p_i$	$p_ix_i$
$0$	$m$	$0$
$1$	$k$	$k$
$2$	$0.3$	$0.6$
$3$	$2k$	$6k$

Download our appand get started for free

Similar Questions

Download our app
and get started for free