मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Solve the following : Identify the random variable as either discrete or continuous in each of the following. Write down the range of it. Amount of syrup prescribed by physician. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Solve the following :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

Amount of syrup prescribed by physician.

बेरीज

उत्तर

Let X = amount of syrup prescribed by a physician.

Then X takes uncountable infinite values.

∴ random variable X is continuous.

shaalaa.com
Probability Distribution of Discrete Random Variables
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Probability Distributions - Miscellaneous Exercise 2 [पृष्ठ २४२]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
पाठ 7 Probability Distributions
Miscellaneous Exercise 2 | Q 1.2 | पृष्ठ २४२

संबंधित प्रश्‍न

State if the following is not the probability mass function of a random variable. Give reasons for your answer.

X 0 1 2 3 4
P(X) 0.1 0.5 0.2 − 0.1 0.2

Find the mean number of heads in three tosses of a fair coin.


Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the standard deviation of X.


Choose the correct option from the given alternative:

Find expected value of and variance of X for the following p.m.f.

X -2 -1 0 1 2
P(x) 0.3 0.3 0.1 0.05 0.25

Solve the following :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

The person on the high protein diet is interested gain of weight in a week.


Solve the following :

The following probability distribution of r.v. X

X=x -3 -2 -1 0 1 2 3
P(X=x) 0.05 0.1 0.15 0.20 0.25 0.15 0.1

Find the probability that

X is positive


Solve the following problem :

A fair coin is tossed 4 times. Let X denote the number of heads obtained. Identify the probability distribution of X and state the formula for p. m. f. of X.


The following is the c.d.f. of r.v. X

x -3 -2 -1 0 1 2 3 4
F(X) 0.1 0.3 0.5 0.65 0.75 0.85 0.9

*1

P (–1 ≤ X ≤ 2)


Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f

f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise.

Calculate: P(0.5 ≤ x ≤ 1.5)


Find expected value and variance of X, the number on the uppermost face of a fair die.


Find k if the following function represents the p. d. f. of a r. v. X.

f(x) = `{(kx,  "for"  0 < x < 2),(0,  "otherwise."):}`

Also find `"P"[1/4 < "X" < 1/2]`


Given that X ~ B(n,p), if n = 10, E(X) = 8, find Var(X).


The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.


X is r.v. with p.d.f. f(x) = `"k"/sqrt(x)`, 0 < x < 4 = 0 otherwise then x E(X) = _______


If F(x) is distribution function of discrete r.v.x with p.m.f. P(x) = `(x - 1)/(3)` for x = 0, 1 2, 3, and P(x) = 0 otherwise then F(4) = _______.


State whether the following is True or False :

If P(X = x) = `"k"[(4),(x)]` for x = 0, 1, 2, 3, 4 , then F(5) = `(1)/(4)` when F(x) is c.d.f.


State whether the following is True or False :

x – 2 – 1 1 2
P(X = x) 0.2 0.3 0.15 0.25 0.1

If F(x) is c.d.f. of discrete r.v. X then F(–3) = 0


State whether the following is True or False :

If p.m.f. of discrete r.v. X is

x 0 1 2
P(X = x) q2 2pq p2 

then E(x) = 2p.


If r.v. X assumes values 1, 2, 3, ……. n with equal probabilities then E(X) = `("n" + 1)/(2)`


Solve the following problem :

The probability distribution of a discrete r.v. X is as follows.

X 1 2 3 4 5 6
(X = x) k 2k 3k 4k 5k 6k

Find P(X ≤ 4), P(2 < X < 4), P(X ≤ 3).


Solve the following problem :

Find the expected value and variance of the r. v. X if its probability distribution is as follows.

x 1 2 3
P(X = x) `(1)/(5)` `(2)/(5)` `(2)/(5)`

Solve the following problem :

Find the expected value and variance of the r. v. X if its probability distribution is as follows.

x – 1 0 1
P(X = x) `(1)/(5)` `(2)/(5)` `(2)/(5)`

Solve the following problem :

Find the expected value and variance of the r. v. X if its probability distribution is as follows.

X 0 1 2 3 4 5
P(X = x) `(1)/(32)` `(5)/(32)` `(10)/(32)` `(10)/(32)` `(5)/(32)` `(1)/(32)`

If a d.r.v. X takes values 0, 1, 2, 3, … with probability P(X = x) = k(x + 1) × 5–x, where k is a constant, then P(X = 0) = ______


If a d.r.v. X has the following probability distribution:

X 1 2 3 4 5 6 7
P(X = x) k 2k 2k 3k k2 2k2 7k2 + k

then k = ______


Find the expected value and variance of r.v. X whose p.m.f. is given below.

X 1 2 3
P(X = x) `1/5` `2/5` `2/5`

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as number greater than 4 appears on at least one die.


E(x) is considered to be ______ of the probability distribution of x.


The probability distribution of a discrete r.v.X is as follows.

x 1 2 3 4 5 6
P(X = x) k 2k 3k 4k 5k 6k

Complete the following activity.

Solution: Since `sum"p"_"i"` = 1

k = `square`


The following function represents the p.d.f of a.r.v. X

f(x) = `{{:((kx;, "for"  0 < x < 2, "then the value of K is ")),((0;,  "otherwise")):}` ______ 


The value of discrete r.v. is generally obtained by counting.


The p.m.f. of a random variable X is as follows:

P (X = 0) = 5k2, P(X = 1) = 1 – 4k, P(X = 2) = 1 – 2k and P(X = x) = 0 for any other value of X. Find k.


Given below is the probability distribution of a discrete random variable x.

X 1 2 3 4 5 6
P(X = x) K 0 2K 5K K 3K

Find K and hence find P(2 ≤ x ≤ 3)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×