The police plans to enforce speed limits by using radar traps of 4 different locations within the city. The radar traps at each of the locations and
are operated 40 % 30% 20% and 30%, of time. If a person who is speeding on h, is way to work has probabilities of 0.2, 0.1, 0.5 and 0.2 respectively of passing through these locations. What is the probability that the person will receive a speeding challan.
To solve this problem numerically, we use the law of total probability. Let: - \( L_1, L_2, L_3, L_4 \) be the four locations. - \( P(L_i) \) _________ ________ ____ _________ _______ _________ ______ _______ ______ _________ ________ ___.
__________ ___ _________ _________ ____ _______ _________ ____ ____ _______ _____.
________ ________ __________ _____ _________ ___ ___.
___ _____ __________ ____ ________ ___ ____.
___ ________ ___ __________ _______ ___ ____ ______ ___ ________.
____ ________ ______ _______ ________ __________ ______ _______ ______ __________.
___ _____ _____ ______ ______ _____ ________ ______ _____ ___ _______ _______.
___ _______ __________ ______ _____ __________ _____ ___ ________.
_______ _____ ____ ______ _____ ___ ______ ______ ________ ___ ____ __________.
_____ _______ _____ ______ _____ _________ _____ __________ _______ __________.
_______ ______ ____ _________ ___ ________ _________.
_____ ________ _________ ______ ____ ____ _______.
________ _________ ______ _____ _________ _______.
_____ _______ _______ ____ __________ ___ _______.
__________ ______ __________ _______ ______ ___ _______ ______ ________ ____ _______ __________.
____.
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The police plans to enforce speed limits by using radar traps of 4 different locations within the city. The radar traps at each of the locations and
are operated 40 % 30% 20% and 30%, of time. If a person who is speeding on h, is way to work has probabilities of 0.2, 0.1, 0.5 and 0.2 respectively of passing through these locations. What is the probability that the person will receive a speeding challan.
A single observation was taken from a population with p.d.f.
Obtain confidence interval for θ.
An unbiased die is rolled twice. Let denote the event: odd face roll on the first die,
denote the event that total score is Odd. Check the independence of
and .
Draw the cumulative frequency curves for the following distribution:
| Marks | No. of Students |
| 0 – 10 | 4 |
| 10 – 20 | 8 |
| 20 – 30 | 11 |
| 30 – 40 | 15 |
| 40 – 50 | 12 |
| 50 – 60 | 6 |
| 60 – 70 | 3 |
Let p be the probability that a coin will fall head in a single toss in order to test against
The coin is tossed 3 times and
is rejected if more than 2 heads are obtained. Find the probability of type I and type II errors. Also obtain the power of the test.
X , X and X3 is a random sample of size 3 from a population with mean µ and variance
. and
are the estimators to estimate µ, and are given by ;
and
i) Are T1 and T2 unbiased? Give reason.
ii) Find the value of λ such that T3 is unbiased.
iii) Which is the best estimator? State giving reasons.
If x has an exponential distribution with parameter θ . Find the density function of