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Probability Theory and Mathematical Statistics Final examination Variant 11 1. If the probability that a newborn baby is a boy is 0.52, what is the probability that 1) there will be 50 boys in 100 births; 2) there will be fewer boys than girls in 100 births? 2. A and B are friends. They decide to meet between 15PM and 17PM on a given day. There is a condition that if A arrives first, he will not wait for B for more than 15min, but if B arrives first, he will not wait for A for more than 30min. What is the probability that they will not meet each other? Part 2. Random Variables 3. A vaccine takes on average 5 years to be developed, the time of development is distributed exponentially. What is the probability that against a certain disease a vaccine will be developed in two years? 4. X is a continuous random variable with the probability density function: f(x)={ax2.75,0,ifx1ifx