###### Advertisements

###### Advertisements

**Solve the following problem :**

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

Amount of syrup prescribed by a physician.

###### Advertisements

#### Solution

Let X = amount of syrup prescribed by a physician.

Here, X can take any positive or fractional value, i.e, X takes uncountably infinite values.

∴ X is a continuous r.v.

#### APPEARS IN

#### RELATED QUESTIONS

Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.

f (x) = k `(4 – x^2 )`, for –2 ≤ x ≤ 2 and = 0 otherwise.

P(x > 0)

Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.

`"f(x)" = {("k"(4 - x^2) "for –2 ≤ x ≤ 2,"),(0 "otherwise".):}`

P(–1 < x < 1)

Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.

f (x) = k `(4 – x^2)`, for –2 ≤ x ≤ 2 and = 0 otherwise.

P (–0·5 < x or x > 0·5)

The following is the p.d.f. of continuous r.v.

f (x) = `x/8`, for 0 < x < 4 and = 0 otherwise.

Find expression for c.d.f. of X

The following is the p.d.f. of continuous r.v.

f (x) = `x/8` , for 0 < x < 4 and = 0 otherwise.

Find F(x) at x = 0·5 , 1.7 and 5

Given the p.d.f. of a continuous r.v. X , f (x) = `x^2/3` ,for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find

P( x < 1)

Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2 /3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P( x < –2)

Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2/3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P(1 < x < 2)

Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2/ 3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P( X > 0)

**Choose the correct option from the given alternative:**

If the 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 |

k =

**Solve the following :**

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

An economist is interested the number of unemployed graduate in the town of population 1 lakh.

The p.m.f. of a r.v. X is given by P (X = x) =`("" ^5 C_x ) /2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise.

Then show that P (X ≤ 2) = P (X ≥ 3).

In the p.m.f. of r.v. X

X |
1 | 2 | 3 | 4 | 5 |

P (X) |
`1/20` | `3/20` | a | 2a | `1/20` |

Find a and obtain c.d.f. of X.

**Solve the following problem :**

A player tosses two coins. He wins ₹ 10 if 2 heads appear, ₹ 5 if 1 head appears, and ₹ 2 if no head appears. Find the expected value and variance of winning amount.

It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64), "for" 0 ≤ x ≤ 4),(0, "otherwise."):}`

Verify whether f(x) is a p.d.f.

It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64), "for" 0 ≤ x ≤ 4),(0, "otherwise."):}`

Find P(0 < X ≤ 1).

It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64), "for" 0 ≤ x ≤ 4),(0, "otherwise."):}`

Find probability that X is between 1 and 3..

F(x) is c.d.f. of discrete r.v. X whose p.m.f. is given by P(x) = `"k"^4C_x` , for x = 0, 1, 2, 3, 4 and P(x) = 0 otherwise then F(5) = _______

**Fill in the blank :**

The values of discrete r.v. are generally obtained by _______

**Fill in the blank :**

The value of continuous r.v. are generally obtained by _______

**Solve the following problem :**

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

An economist is interested in knowing the number of unemployed graduates in the town with a population of 1 lakh.

**Solve the following problem :**

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

A highway safety group is interested in the speed (km/hrs) of a car at a check point.

c.d.f. of a discrete random variable X is

Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is ______.

Three fair coins are tossed simultaneously. Find the probability mass function for a number of heads that occurred

A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the probability mass function

A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the cumulative distribution function

A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find P(X ≥ 6)

Find the probability mass function and cumulative distribution function of a number of girl children in families with 4 children, assuming equal probabilities for boys and girls

Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by

`f(x) = {{:((x^2 + 1)/k"," "for" x = 0"," 1"," 2),(0"," "otherwise"):}`

Find cumulative distribution function

Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by

`f(x) = {{:((x^2 + 1)/k"," "for" x = 0"," 1"," 2),(0"," "otherwise"):}`

Find P(X ≥ 1)

The cumulative distribution function of a discrete random variable is given by

F(x) = `{{:(0, - oo < x < - 1),(0.15, - 1 ≤ x < 0),(0.35, 0 ≤ x < 1),(0.60, 1 ≤ x < 2),(0.85, 2 ≤ x < 3),(1, 3 ≤ x < oo):}`

Find the probability mass function

A random variable X has the following probability mass function.

x |
1 | 2 | 3 | 4 | 5 |

F(x) |
k^{2} |
2k^{2} |
3k^{2} |
2k | 3k |

Find the value of k

A random variable X has the following probability mass function.

x |
1 | 2 | 3 | 4 | 5 |

F(x) |
k^{2} |
2k^{2} |
3k^{2} |
2k | 3k |

Find P(2 ≤ X < 5)

A random variable X has the following probability mass function.

x |
1 | 2 | 3 | 4 | 5 |

F(x) |
k^{2} |
2k^{2} |
3k^{2} |
2k | 3k |

Find P(X > 3)

The cumulative distribution function of a discrete random variable is given by

F(x) = `{{:(0, "for" - oo < x < 0),(1/2, "for" 0 ≤ x < 1),(3/5, "for" 1 ≤ x < 2),(4/5, "for" 2 ≤ x < 4),(9/5, "for" 3 ≤ x < 4),(1, "for" ≤ x < oo):}`

Find the probability mass function

The cumulative distribution function of a discrete random variable is given by

F(x) = `{{:(0, "for" - oo < x < 0),(1/2, "for" 0 ≤ x < 1),(3/5, "for" 1 ≤ x < 2),(4/5, "for" 2 ≤ x < 4),(9/5, "for" 3 ≤ x < 4),(1, "for" ≤ x < oo):}`

Find P(X < 3)

The cumulative distribution function of a discrete random variable is given by

F(x) = `{{:(0, "for" - oo < x < 0),(1/2, "for" 0 ≤ x < 1),(3/5, "for" 1 ≤ x < 2),(4/5, "for" 2 ≤ x < 4),(9/5, "for" 3 ≤ x < 4),(1, "for" ≤ x < oo):}`

Find P(X ≥ 2)

If Xis a.r.v. with c.d.f F (x) and its probability distribution is given by

X = x | - 1.5 | -0.5 | 0.5 | 1.5 | 2.5 |

P(X = x) | 0.05 | 0.2 | 0.15 | 0.25 | 0.35 |

then, F(1.5) - F(- 0.5) = ?

Choose the correct alternative:

Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with Probability 0.5. Assume that the results of the flips are independent and let X equal the total number of heads that result. The value of E[X] is

Choose the correct alternative:

Suppose that X takes on one of the values 0, 1 and 2. If for some constant k, P(X = i) = kP(X = i – 1) for i = 1, 2 and P(X = 0) = `1/7`. Then the value of k is

Let X = time (in minutes) that lapses between the ringing of the bell at the end of a lecture and the actual time when the professor ends the lecture. Suppose X has p.d.f.

f(x) = `{(kx^2"," 0 ≤ x ≤ 2), (0"," "othenwise"):}`

Then, the probability that the lecture ends within 1 minute of the bell ringing is ______

The p.m.f. of a random variable X is

P(x) = `(5 - x)/10`, x = 1, 2, 3, 4

= 0, otherwise

The value of E(X) is ______

If the probability function of a random variable X is defined by P(X = k) = a`((k + 1)/2^k)` for k - 0, 1, 2, 3, 4, 5, then the probability that X takes a prime value is ______

A card is chosen from a well-shuffled pack of cards. The probability of getting an ace of spade or a jack of diamond is ______.

The p.d.f. of a continuous random variable X is

f(x) = 0.1 x, 0 < x < 5

= 0, otherwise

Then the value of P(X > 3) is ______

Two cards are randomly drawn, with replacement. from a well shuffled deck of 52 playing cards. Find the probability distribution of the number of aces drawn.

At random variable X – B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are ______.

For the following distribution function F(x) of a rv.x.

x | 1 | 2 | 3 | 4 | 5 | 6 |

F(x) | 0.2 | 0.37 | 0.48 | 0.62 | 0.85 | 1 |

P(3 < x < 5) =

If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to ______.