Expressing "to wait" with 期待 and 等待
Both verbs mean “to wait", but they have different connotations.
The verbs 期待 
and 等待 mean “to wait” and “to expect”.
The verb 等待 has a neutral meaning, and the verb 期待 means “to look forward to”.
and 等待 mean “to wait” and “to expect”.
The verb 等待 has a neutral meaning, and the verb 期待 means “to look forward to”. Pay attention
Both verbs are most commonly used in a written language.
Examples
我期待你这学期功课有进步
I am looking forward to your success in this term
wǒ qīdài nǐ zhè xuéqí gōngkè yǒu jìnbù
满怀期待的一群人聚在了一起
The group of people who are waiting for the meeting has gathered together
mǎnhuái qídài de yì qún rén jù zài le yìqǐ
他正在等待医生的诊断结论
They are waiting for the doctor’s diagnosis
tāmen zhèngzài děngdài yīshēng de zhěnduàn jiélùn
我们只好等待了
All we have to do is wait
wǒmen zhǐhǎo děngdài le