Let W be a random variable giving the number of tails minus the number of heads in three tosses of a coin. Assuming that a tail is three times as likely to occur, find the probability distribution of the random variable W.

Explanation:

In a toss of a coin; the are two possibilities of events happening;

Either a Head or a Tail.

Given data:

Let W be a random variable giving the number of tails minus the number of heads in three tosses of a coin.

So; W = [ HHH, HHT, HTH, HTT, TTT, THT, TTH , THH]

Probability distribution of the random variable W for  a tail occurring at three coin will be

W = 3: P(3T)

= P (TTT)

=

=

W = 2 : P(2T, 1H)

= P( HTT, TTH, THT)

= ×

=

=

W = 1 : P(1T, 2H)

= P ( HHT, HTH, THH)

= ×

=

=

W = 0 : P (3H)

= P (HHH)  

=

=

air, water, heat and noise pollution can all be caused by producing and using technology. consuming resources - non-renewable resources, including precious metals like gold, are used to make technology

americans began to notice growing differences between the northern and southern sections of the country. there were more people living in cities in the north, which made it more urban. more people lived on farms in the south, which made it more rural. while many people were farmers in the northern states, there were now other ways to make a living, such as working in mechanical cotton gins factories manufacturing cloth, tools and other goods. people in the north supported high tariffs on goods imported from europe because the extra cost encouraged people to “buy american” instead. in the southern states, planters did not like tariffs because they sold most of their production to europe and bought their tools from there as well. southerners believed the protective tariff was something that only northern factory owners keep their profits high. so the southern politicians came up with an idea. they would opt out. they would simply ignore the protective tariff. it was ‘null and void’ in south carolina. the state would not collect the taxes on goods imported into south carolina, no matter what the president said they had to do. this decision led to the nullification crisis.